CAFFREY, Senior District Judge.
The defendant Alfreda Barnes appeals her conviction in the District of Rhode Island for possession with intent to distribute cocaine base in violation of 21 U.S.C. § 841(a)(1) (Count I) and for possession, as a convicted felon, of a firearm in violation of 18 U.S.C. § 922(g) (Count II). On appeal, Barnes challenges her conviction for Count I on three grounds. First, Barnes claims that there was insufficient evidence to support the jury’s finding that she constructively possessed the cocaine base found in her apartment. Second, Barnes argues that there was insufficient evidence to prove that the mixture of cocaine base weighed more than 50 grams as required by § 841(b)(l)(A)(iii). Third, Barnes contends that the term “cocaine base” as used in 21 U.S.C. § 841 (b)(1)(A)(iii) is unconstitutionally vague in violation of the fifth amendment. Finally, as to both Count I and Count II, Barnes challenges her convictions claiming that the district court erred in defining reasonable doubt in its jury instructions. After a thorough review of the trial record and the appellant’s arguments, we affirm the appellant’s convictions on both counts.
I.
The relevant facts for this appeal are those presented to the jury during the appellant’s three-day trial. The trial testimony centered on the seizure of 72.5 grams of “crack” cocaine and a semi-automatic rifle from an apartment at 212 Lenox Avenue in Providence, Rhode Island. According to the record, the jury heard the testimony of 12 witnesses and reviewed at least 14 exhibits. The trial evidence is summarized as follows.
At approximately 11:45 p.m. on June 29, 1987, seven officers of the Providence Police Department executed a search warrant for the second floor apartment at 212 Le-nox Avenue. Upon arriving at the address, Detective Sergeant Joseph Fusco found the appellant Alfreda Barnes in the driveway beside 212 Lenox Avenue. Fusco informed Barnes of the warrant and asked if he could enter the apartment, but Barnes refused to allow entry.
At this time, Fusco saw a young woman in the second floor window of the building. Fusco told the young woman he had a search warrant and asked to be let in, but he received no response. The police officers then forcibly entered both the front door to the building and the door to the second floor apartment.
The police found the second floor apartment empty. Upon entering, the police came to a living room which was partitioned into a double parlor area. Beyond the living room was the kitchen, and off the kitchen was a pantry area. There were to back, and one bedroom off the living room front. The police never searched the bedroom in front.
Detective Sergeant Thomas Oates and Fusco searched the larger rear bedroom. The room had a large mahogany water bed with storage drawers underneath. Beside the bed was a matching bureau, and, at the base of the bed, was a television with several shelves underneath. The room also had a hamper and a closet with female clothing in it.
The police seized several items from the larger rear bedroom. On the floor next to the bed, Fusco found a semi-automatic Sturm Ruger mini-14 rifle modified with a flash-suppressor and a loaded 20-round magazine. In the bureau, Fusco found another gun magazine filled with live ammunition and a box containing $588 in cash. In the hamper, Oates discovered a blue Baby Fresh tissue container with $5,948 in cash inside. With the money, there was also a slip of paper with the figure “$6,000” and other scribblings written on it. Oates also found certain paperwork on the shelves below the television. Among these papers were two food stamp cards: one had the name “A. Barnes” and the other had the name “G. Barnes.”
Under the television, Oates noticed a Mrs. Filbert’s margarine container wrapped with a rubber band. Inside, Oates found three rock-like objects: one the size of a baseball, the other two the size of golf balls. Oates seized these objects believing them to be “crack” cocaine.
After starting to search the larger rear bedroom. Fusco took the rifle into the kitchen where various items were being inventoried. At that time, Barnes was in custody and seated by the kitchen table. As Fusco entered the kitchen with the rifle, Barnes said: “That’s mine, you can’t take it, I bought it at D & B Guns.”
Detective Gail Zienowicz and Fusco searched the kitchen and pantry areas. Zienowicz found several hundred unused small plastic vials inside a clothes dryer in the kitchen. Zienowicz seized the vials believing them to be “crack vials” used for distributing “crack” cocaine. Fusco also found and seized two triple beam scales in the pantry area.
During the search, the police assembled three individuals in the kitchen: Barnes who was in the driveway, the young woman who Fusco recognized as the person in the window, and a small infant. Barnes was arrested and taken into custody by the police. The police did not identify the young woman or the infant.
At trial, Lulu Barnes, the appellant Alfreda Barnes’s mother who lived on the first floor and owned the building, testified as the sole defense witness. Lulu said that Alfreda had lived in the second floor apartment for nine years. Alfreda had paid rent of $870 a month for several years and was on welfare with “section 8” housing support. Lulu also said the phone service was subscribed in Alfreda’s name.
Lulu Barnes testified that Alfreda lived in the second-floor apartment with her .infant child, not named in the record, and her two older children Gina, 20, and Marvin, 18. Marvin was a student at the University of Rhode Island and did not stay at the apartment regularly. The infant and Gina were staying at the apartment at the time.
Lulu Barnes also testified that Gina, not Alfreda, slept in the larger rear bedroom where the rifle and cocaine base were found. Lulu said that Alfreda slept with the infant in the smaller front bedroom off the living room. This testimony, however, was not unequivocal. On cross-examination, Lulu admitted that she had first said Gina lived in the smaller front bedroom, and then quickly corrected herself.
Finally, concerning the substance seized, a Drug Enforcement Administration forensic chemist, Andrea Michaels, testified at trial that she analyzed the three chunks found in the apartment. First, she weighed the three chunks and determined their weight to be 72.5 grams. Next, she screened each chunk with a common chemical color test and found each to contain some amount of cocaine. Then, she ground the chunks into a uniform powder and performed infra-red spectrography and gas chromatography tests on a one gram sample. Michaels said her test results showed the powder to contain 97 percent pure cocaine base. In terms of her chemistry training, Michaels explained that cocaine base differs from cocaine hydrochloride in its molecular structure. Michaels said that cocaine base is commonly called “crack” cocaine which is generally smoked.
II.
The first issue presented by this appeal is whether there was sufficient evidence to support the jury finding that the appellant Barnes constructively possessed the cocaine base found in the larger rear bedroom. Barnes argues that the only direct testimony offered at trial showed that her daughter Gina lived in the larger rear bedroom, and thus Barnes could not have constructively possessed the drugs found in the rear bedroom. Further, Barnes contends that the drugs and drug paraphernalia seized in other areas of the apartment were not in plain view, and thus she had no knowledge or control over these items. In light of the full record and the applicable law, these arguments are not persuasive.
In reviewing this issue, the court must decide whether “after viewing the evidence in the light most favorable to the prosecution, any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt.” Jackson v. Virginia, 443 U.S. 307, 319, 99 S.Ct. 2781, 2789, 61 L.Ed.2d 560 (1979) (emphasis in original). See also United States v. Serrano, 870 F.2d 1, 5 (1st Cir.1989); United States v. Torres Lopez, 851 F.2d 520, 527 (1st Cir.1988), cert. denied, - U.S.-, 109 S.Ct. 1144, 103 L.Ed.2d 204 (1989). In considering this question, the court shall draw all reasonable inferences from direct and circumstantial evidence in favor of the government. United States v. Lochan, 674 F.2d 960, 965-66 (1st Cir.1982). Furthermore, given this circuit’s adherence to the “waiver rule” concerning mid-trial motions for acquittal, the court shall consider all the evidence presented at trial both from the government and the defendant. United States v. Notarantonio, 758 F.2d 777, 788 (1st Cir.1985). Nevertheless, the court is mindful that the burden remains on the government to prove every element of the offense beyond a reasonable doubt. Lochan, 674 F.2d at 965-66.
Pursuant to 21 U.S.C. § 841(a), the government was required to prove that Barnes knowingly possessed the cocaine base found in the apartment at 212 Lenox Avenue. The government need not prove actual possession; constructive possession is sufficient. See United States v. Calle-Cardenas, 837 F.2d 30, 32 (1st Cir.), cert. denied, 485 U.S. 1024, 108 S.Ct. 1582, 99 L.Ed.2d 897 (1988); United States v. Matra, 841 F.2d 837, 840 (8th Cir.1988); United States v. Carrasco, 830 F.2d 41, 45 (5th Cir.1987). To show constructive possession, the government must prove that Barnes had dominion and control over area where the contraband was found. See United States v. Morales, 868 F.2d 1562, 1573 (11th Cir.1989); Matra, 841 F.2d at 840. Constructive possession may be shown by direct or circumstantial evidence, but mere association or mere presence with one who possessed contraband is not enough. See United States v. Castillo, 844 F.2d 1379 (9th Cir.1988); Carrasco, 830 F.2d at 45. See also United States v. Mehtala, 578 F.2d 6, 9-10 (1st Cir.1978). Finally, knowledge of possession may similarly be inferred by demonstrating dominion and control over the area where contraband is found. Lochan, 674 F.2d at 966.
To begin our analysis, we note that the appellant misconstrues the law concerning constructive possession on two points. First, Barnes argues in her brief that she “did not have exclusive access to the apartment,” and further suggests that the government must show Barnes exclusively occupied the larger bedroom to satisfy its burden. While the government may prove its case in this manner, constructive possession may be proven in situations of joint occupancy and it need not be exclusive. See Calle-Cardenas, 837 F.2d at 32 (defendant found in apartment with two other men similarly clothed had dominion and control over apartment); United States v. Poole, 878 F.2d 1389, 1392 (11th Cir.1989) (defendant living in apartment with sister, three adolescent children, and a male friend had dominion and control over apartment). Second, the appellant suggests that the government must prove her dominion and control over the cocaine base itself. Again the government may prove its case in that way, but the government may also satisfy its burden of proof by showing dominion and control over the area where the contraband was found. See Morales, 868 F.2d at 1573 (defendant leasing apartment had dominion and control over drugs found there); Lochan, 674 F.2d at 966 (defendant driving vehicle had dominion and control over hashish found behind back seat).
Thus, the issue reduces itself to whether the appellant Barnes, either jointly or exclusively, had dominion and control over the area where the cocaine base was found. With multiple occupants in the apartment and Lulu Barnes’s testimony, the evidence as presented to the jury created a question of fact as to who had dominion and control over the larger rear bedroom. On appeal, however, the evidence presented at trial creates no question of law concerning whether the jury had a rational basis for its verdict.
The government presented substantial circumstantial evidence that Barnes had dominion and control over the larger rear bedroom. The police found a loaded rifle, which admittedly belonged to Barnes, on the floor in the larger rear bedroom and seized a loaded magazine for the gun from the bureau in the same room. The police also found Barnes’s food stamp identification card in the bedroom with her name on it. In addition, the bedroom closet contained women’s clothing.
Added to this circumstantial evidence, certain reasonable inferences could be drawn from these facts. While Barnes argues that her daughter lived in the larger rear bedroom, it is unlikely that Barnes would leave her loaded rifle on the floor of her daughter’s room or store ammunition for the rifle in her daughter’s bureau. Moreover, the size and furnishings of the larger rear bedroom, as well as its proximity to the infant’s room, are consistent with the occupant being the head-of-household with a young child.
In addition to the larger rear bedroom, Barnes clearly had dominion and control over the entire apartment. Barnes had leased the apartment for nine years and the phone was subscribed in her name. Barnes, as the mother of all the regular occupants, was the head of the family in the apartment. Further, Barnes, as a welfare recipient with three dependents, was also the head-of-the household.
Added to this evidence of dominion and control, the government offered further circumstantial evidence suggesting Barnes had knowledge of a large scale drug operation at work in the apartment. The police seized several hundred unused “crack” vials from the clothes dryer in the kitchen. In the pantry, the police found two triple-beam scales commonly used in drug operations. The police discovered over $6,000 cash in an apartment leased by a welfare recipient. Further, the police seized more than 70 grams of “crack” cocaine in close proximity to a loaded, semi-automatic rifle in the apartment.
In response, Barnes mounts several arguments. First, she argues that the testimony of Lulu Barnes was uncontroverted, and Lulu told the jury that Gina, not Alfreda, lived in the larger rear bedroom. But clearly, the fact that Lulu’s testimony was initially ambiguous, as admitted on cross-examination, creates a question of credibility for the jury. Thus, this testimony presented the jury with the task of weighing the credibility of a witness against the reasonable inferences of the government’s circumstantial case. This task was properly before the jury, and, on review, there appears to be ample evidence to support a verdict in favor of either the government or Barnes.
Second, Barnes contends that her identification card was found with her daughter Gina’s card, thus showing a potential conflict in the circumstantial evidence presented by the government. But this response, merely frames the issues placed before the jury, and it does not negate the government’s theory of dominion and control. On appeal, we cannot say that the jury had no rational basis for their verdict.
Third, Barnes argues that most of the circumstantial evidence was not in plain view, and therefore Barnes may not have had knowledge of its existence despite living in the apartment. But clearly the rifle, found beside the bed, and the triple beam scales, found in the pantry, were in plain view. Moreover, it may be arguable that the vials found in the clothes dryer and the cocaine base found in the margarine container were sufficiently in common areas to impute knowledge to the tenant and head-of-household living in the apartment. Nonetheless, we need not answer these specific factual questions because Barnes’s arguments do no more than raise issues for consideration by a jury, and, so long as the jury had a rational basis for its conclusions, we must affirm their verdict.
In sum, we find that on a thorough review of all the circumstantial evidence and the reasonable inferences drawn from that evidence, there is sufficient evidence to support the jury verdict.
III.
The next issue presented by this appeal is whether the government presented sufficient evidence to prove the cocaine base mixture weighed more than 50 grams as required by 21 U.S.C. § 841(b)(l)(A)(iii). The appellant Barnes argues that the government failed to test separately each chunk of cocaine found in the apartment, and therefore, it is possible that one of the three chunks did not contain any cocaine base. Further, if that chunk without cocaine base weighed more than 22.5 grams, the court could not find that at least 50 grams of the 72.5 grams seized contained cocaine base. These arguments, however, fail to consider the express language of 21 U.S.C. § 841(b) and the purity of the cocaine seized.
This issue focuses on the mandatory penalty provisions of 21 U.S.C. § 841(b). If a person knowingly possesses a controlled substance with intent to distribute, such person shall serve a mandatory term of imprisonment depending on the quantity and type of controlled substance. 21 U.S.C. § 841(b). Under subsection (b)(l)(A)(iii), a mandatory 10-year sentence shall apply to violations involving “50 grams or more of a mixture of substance described in clause (ii) which contains cocaine base.” Clause (ii) describes various forms of coca leaves, cocaine, and its derivatives. 21 U.S.C. § 841(b)(l)(A)(ii).
In this case, the DEA chemist testified that all three chunks together weighed 72.5 grams. The chemist also testified that each chunk contained some cocaine and, after being ground into a uniform mixture, the chunks in fact contained cocaine base. Further, the chemist testified that the mixture was 97 percent pure cocaine base.
This evidence is clearly sufficient to satisfy the penalty provisions of section 841(b)(1)(A). The express statute does not require the violation to involve 50 grams of cocaine base; rather it applies to “50 grams of a mixture or substance [of cocaine] which contains cocaine base.” Thus, where the sample weighs 72.5 grams and the mixture contains 97 percent pure cocaine base, the evidence is clearly sufficient for the court to find the contraband seized satisfied the penalty provisions of section 841(b)(l)(A)(iii).
IV.
The next issue presented by this appeal is whether the term “cocaine base” as used in 21 U.S.C. § 841(b)(l)(A)(iii) is so vague as to violate the due process clause of the fifth amendment. The appellant Barnes points out that the term “cocaine base” was included in the statute without any definition. Further, Barnes claims the word “base” appears with several definitions in any traditional dictionary, and consequently, the term “cocaine base” may be subject to any number of possible interpretations creating a vagueness problem. We, however, disagree.
The court recognizes the well-established principle that due process requires a penal statute to “define [a] criminal offense with sufficient definiteness that ordinary people understand what conduct is prohibited and in a manner that does not encourage arbitrary and discriminatory enforcement.” Kolender v. Lawson, 461 U.S. 352, 357, 103 S.Ct. 1855, 1858, 75 L.Ed.2d 903 (1983). This “void for vagueness” doctrine, however, does not mean a statute is unconstitutionally vague where “Congress might, without difficulty, have chosen ‘clearer and more precise language’ equally capable of achieving the end which it sought.” United States v. Powell, 423 U.S. 87, 94, 96 S.Ct. 316, 321, 46 L.Ed.2d 228 (1975) (quoting United States v. Petrillo, 332 U.S. 1, 7, 67 S.Ct. 1538, 1541, 91 L.Ed. 1877 (1947)). Finally, where the first amendment is not implicated, a “void for vagueness” challenge must be unconstitutional as applied to the defendant and “must be examined in light of the facts of the case at hand.” United States v. Mazurie, 419 U.S. 544, 550, 95 S.Ct. 710, 714, 42 L.Ed.2d 706 (1975).
To begin our analysis, the term “cocaine base” clearly defines a substance differing from other forms of cocaine. The DEA chemist at trial testified that “cocaine base” was chemically distinguishable from “cocaine hydrochloride.” Cocaine hydrochloride is water soluble, formed in crystals or flakes, and generally snorted by users. Cocaine base is not water soluble, concentrated in a hard rock-like form, and generally smoked. This testimony is consistent with the sources reviewed by this court. See M. Ellenhorn & D. Barcelona, Medical Toxicology: Diagnosis and Treatment of Human Poisoning 645-48 (1988); 3 Court Room Toxicology (MB) Coca 1-2 (1987) (eds. Houts, Baselt, Cravey); Blakiston’s Gould Medical Dictionary 290 (5th ed. 1979). See also United States v. Brown, 859 F.2d 974, 975-76 (D.C.Cir.1988).
Further, in this case, there is no question that the possession of the substance in question is specifically what Congress intended to punish. The chunks seized were the form of cocaine known as “crack,” which was a primary target of the Narcotics Penalties and Enforcement Act of 1986. See 132 Cong.Rec. S11973 (Aug. 15, 1986) (statement of Sen. D’Amato); 132 Cong.Rec. S14270 (Sept. 30, 1986) (statement of Sen. DeConcini); H.R.Rep. No. 845, 99th Cong., 2d Sess. at 11-12, 17 (1986). The substance at issue is not some new form or derivative of cocaine which was not originally contemplated by Congress. Thus, as applied to the facts of this case, the term “cocaine base” clearly does not violate the defendant’s due process rights.
For all these reasons, the appellant fails to show any “void for vagueness” problem with the term “cocaine base” in 21 U.S.C. § 841(b)(l)(A)(iii).
V.
The final issue raised in this appeal is whether the jury instructions concerning reasonable doubt unconstitutionally lowered the government’s burden of proof. The challenged portion of the district court’s charge is as follows:
Reasonable doubt by definition means a doubt founded upon reason not conjec- or which some reason as opposed to conjecture or speculation can be assigned in your minds. I remind you again that the burden is on the government. It is not a doubt suggested by the ingenuity of counsel and unwarranted by the testimony; nor a doubt borne of merciful inclination to permit the accused to escape conviction; nor a doubt prompted by sympathy for those connected with the defendant.
The appellant Barnes argues that the district court’s negative definition of reasonable doubt impermissibly undermined the burden of proof placed on the government. Particularly, the appellant objects to the definition “not a doubt suggested by the ingenuity of counsel.” Relying on our recent decision in United States v. Glantz, we find the appellant’s arguments unpersuasive.
In Glantz, this court considered nearly identical objections to the same instructions from the same district court. 847 F.2d 1, 11-12 (1st Cir.1988). The Glantz opinion expressly disapproved of the “ingenuity of counsel” language, but found that, in light of other extensive and correct definitions of reasonable doubt, the jury instructions taken as a whole caused no constitutional error. 847 F.2d at 11. See United States v. Glenn, 828 F.2d 855, 861 (1st Cir.1987). We note that here, as in Glantz, the trial record is replete with numerous correct definitions of reasonable doubt. These definitions were given several times throughout the trial and in the jury instructions. In light of these definitions, we do not believe the jury could have been misled and thus find no constitutional error.
For all the reasons stated above, we affirm the appellant’s convictions on both counts.
. Honorable Francis J. Boyle, Chief Judge for the District of Rhode Island presiding.
. At trial, three of the seven officers testified for the government: Detective Sergeant Joseph Fus-co, Detective Sergeant Thomas Oates, and Detective Gail Zienowicz.
. As noted in the appellee's brief, this equivocation was not recorded initially by the court reporter on direct examination. Trial Transcript, Vol. Ill, p. 307. On cross examination, however, Lulu Barnes admitted that she changed her first response:
Q Let me just ask you this question, Miss Barnes, isn’t it a fact that about 20 minutes ago when Mr. O’Brien first asked you who was in that bedroom, whose bedroom that was, you said it was Gina’s?
A I always make, you can make a mistake, it’s not Gina’s.
Q But you did say that?
A I said it but it’s not Gina's. It's Alfreda’s bedroom.
Trial Transcript, Vol. Ill, p. 323.
This fact is further corroborated by observations made by the judge during post-trial motions: "One bit of evidence that's been overlooked by everybody seems to me is the defendant’s mother’s testimony in which she was asked the question as to whose bedroom was the one closest to the front door. As I recall that testimony her response was to the effect that that was Gina’s bedroom. Then she changed it. It became Alfreda’s bedroom.” Trial Transcript, Vol. IV, p. 26.
. Where the defendant makes a motion for acquittal at the close of the government’s case and then again at the close of the defendant’s case, this court deems the mid-trial motion as waived by the defendant. Notarantonio, 758 F.2d at 788; Colella v. United States, 360 F.2d 792, 802 (1st Cir.), cert. denied, 385 U.S. 829, 87 S.Ct. 65, 17 L.Ed.2d 65 (1966). The law of this circuit requires this court to examine all the evidence submitted at trial. Notarantonio, 758 F.2d at 788. In this case, applying the "waiver rule,” we shall consider the testimony of the defense’s sole witness, the defendant's mother Lulu Barnes, in evaluating the sufficiency of evidence for the jury verdict.
. As further support, we note that this decision is consistent with this court’s recent decision in United States v. Calle-Cardenas, 837 F.2d 30, 32 (1st Cir.), cert. denied, 485 U.S. 1024, 108 S.Ct. 1582, 99 L.Ed.2d 897 (1988). In Calle-Cardenas, the defendant was found in the living room of an apartment along with two other individuals. Certain drugs were found on a table in front of the defendant along with the defendant’s identification card. On review of the evidence, the court found that there was sufficient evidence to prove constructive possession by the defendant.
. It is important to note that the court, not the jury, determines the quantity and type of controlled substance appropriate under 21 U.S.C. § 841(b). See United States v. Gohagen, 886 F.2d 1041 (8th Cir.1989); United States v. Padilla, 869 F.2d 372, 381 (8th Cir.), cert. denied, - U.S. -, 109 S.Ct. 3223, 106 L.Ed.2d 572 (1989). Section 841(b) describes the penalty provisions for violations of section 841(a), in this case possession of a controlled substance with intent to distribute. Therefore, as a penalty provision, the district court judge determines the facts at the sentencing, and, on appeal, we review the court's factual findings, not the jury’s verdict.
In this case, the district court judge properly made a finding during the sentencing as to the quantity and type of the cocaine. See Padilla, 869 F.2d at 381 (conviction vacated and remanded for resentencing where district court had not made findings of fact as to the quantity and type of cocaine). At the sentencing hearing, the court stated: “I’m satisfied that the particular quantity of cocaine base as required by the statute has been proven by the government beyond a reasonable doubt. I am satisfied that the nature of the substance was cocaine base, if those findings of fact have to be made at this point in time.” Trial Transcript, Vol. IV, p. 52.
As a final concern, we note that the judge in this case instructed the jury that it must find the defendant possessed “a detectable amount of cocaine base” and "the amount is more than 50 grams” to return a guilty verdict. Trial Transcript, Vol. Ill, pp. 391-92. In fact, questions as to whether the mixture found was cocaine base and its specific weight were factual findings for the judge at sentencing. The jury need only have found that the three chunks seized contained some mixture of cocaine as defined in schedule II. See 21 U.S.C. § 812. This instruction, however, was not harmful or prejudicial since it created a greater burden for the government, not for the defendant. Cf. Padilla, 869 F.2d at 381 n. 5 (court found no prejudice to defendant where indictment improperly cited penalty provisions of 21 U.S.C. § 841(b) as part of substantive elements of the offense).
. At the outset, we note that the use of the term "cocaine base” in this statute does not present a question of giving adequate notice to possible defendants. The challenged term appears in the penalty provisions of 21 U.S.C. § 841(b). As such, the term "cocaine base” is only relevant to enhanced penalties facing a defendant, and Congress added these penalties without altering the substantive elements of 21 U.S.C. § 841(a). See Anti-Drug Abuse Act of 1986, P.L. No. 99-570, 100 Stat. 3207, 3207-2 (1986) (codified as amended at 21 U.S.C. § 841(b)). Thus, Congress did not criminalize any conduct which was not already illegal, and there is no problem of giving adequate notice of enhanced penalties to possible defendants. See United States v. Collado-Gomez, 834 F.2d 280, 281 (2d Cir.1987), cert. denied, 485 U.S. 969, 108 S.Ct. 1244, 99 L.Ed.2d 442 (1988).
In our case, we shall assume that the appellant is challenging the possible vagueness problems in enforcing the term. See Kolender, 461 U.S. at 358, 103 S.Ct. at 1858 (“the more important aspect of the vagueness doctrine ‘is not the actual notice, but the other principal element of the doctrine — the requirement that a legislature establish minimum guidelines to govern law enforcement’ ” (quoting Smith v. Goguen, 415 U.S. 566, 574, 94 S.Ct. 1242, 1248, 39 L.Ed.2d 605 (1974)). Therefore, in our analysis, we shall focus on problem of vagueness in administering and enforcing the statute rather than in giving adequate notice to the defendant.
. The Narcotics Penalties and Enforcement Act of 1986 was passed as subtitle A of title I of the Anti-Drug Abuse Act of 1986. See Anti-Drug Abuse Act of 1986, P.L. No. 99-570, 100 Stat. 3207, 3207-2 (1986) (codified as amended at 21 U.S.C. § 841(b)).
. We also note that three circuit courts of appeals have faced similar constitutional challenges to the same language in the same statute, and all have found that the term “cocaine base” does not create a due process violation. See United States v. Brown, 859 F.2d 974, 975-76 (D.C.Cir.1988); United States v. Collado-Gomez, 834 F.2d 280, 281 (2d Cir.1987), cert. denied, 485 U.S. 969, 108 S.Ct. 1244, 99 L.Ed.2d 442 (1988); United States v. Williams, 876 F.2d 1521, 1525 (11th Cir.1989).
.In reviewing the Glantz and Glenn opinions, we reiterate our disapproval of reasonable doubt defined as "not a doubt suggested by the ingenuity of counsel.” Such a definition "provides an incorrect inference” since “all defenses rely to a great extent on the ingenuity of counsel.” Glantz, 847 F.2d at 11. Further, “[i]f these words stood alone, they could conceivably misdirect the jury’s attention away from the logical force of the doubt and toward its source, leading it to discount reasonable doubts created by defense counsel." Glenn, 828 F.2d at 861 (reviewing similar “ingenuity of counsel” language).
We further note our disapproval of the other language used in the final sentence of the quoted instruction. That too is confusing and incorrect.