opinion: Chief Justice Rehnquist
  delivered the opinion of the Court.
  Section 841(b)(l)(B)(v) of Title 21 of the United States Code calls for a mandatory minimum sentence of five years for the offense of distributing more than one gram of a “mixture or substance containing a detectable amount of lysergic acid diethylamide (LSD).” We hold that it is the weight of the blotter paper containing LSD, and not the weight of the pure LSD, which determines eligibility for the minimum sentence.
  Petitioners Richard L. Chapman, John M. Schoenecker, and Patrick Brumm were convicted of selling 10 sheets (1,000 doses) of blotter paper containing LSD, in violation of § 841(a). The District Court included the total weight of the paper and LSD in determining the weight of the drug to be used in calculating petitioners’ sentences. Accordingly, although the weight of the LSD alone was approximately 50 milligrams, the 5.7 grams combined weight of LSD and blotter paper re-suited in the imposition of the mandatory minimum sentence of five years required by § 841(b)(l)(B)(v) for distributing more than 1 gram of a mixture or substance containing a detectable amount of LSD. The entire 5.7 grams was also used to determine the base offense level under the United States Sentencing Commission, Guidelines Manual (1990) (Sentencing Guidelines). Petitioners appealed, claiming that the blotter paper is only a carrier medium, and that its weight should not be included in the weight of the drug for sentencing purposes. Alternatively, they argued that if the statute and Sentencing Guidelines were construed so as to require inclusion of the blotter paper or other carrier medium when calculating the weight of the drug, this would violate the right to equal protection incorporated in the Due Process Clause of the Fifth Amendment.
  The Court of Appeals for the Seventh Circuit en banc held that the weight of the blotter paper or other carrier should be included in the weight of the “mixture or substance containing a detectable amount” of LSD when computing the sentence for a defendant convicted of distributing LSD. The Court of Appeals also found that Congress had a rational basis for including the carrier along with the weight of the drug, and therefore the statute and the Sentencing Guidelines did not violate the Constitution. United States v. Marshall, 908 F. 2d 1312 (1990). We granted certiorari, 498 U. S. 1011 (1990), and now affirm.
  Title 21 U. S. C. § 841(b)(1)(B) provides that
  “any person who violates subsection (a) of this section [making it unlawful to knowingly or intentionally manufacture, distribute, dispense, or possess with intent to manufacture, distribute, or dispense, a controlled substance] shall be sentenced as follows:
  “(1)(B) In the case of a violation of subsection (a) of this section involving—
  “(v) 1 gram or more of a mixture or substance containing a detectable amount of lysergic acid diethylamide (LSD);
  “such person shall be sentenced to a term of imprisonment .which may not be less than 5 years . . .
  Section 841(b)(1)(A)(v) provides for a mandatory minimum of 10 years’ imprisonment for a violation of subsection (a) involving “10 grams or more of a mixture or substance containing a detectable amount of [LSD].” Section 2D1.1(c) of the United States Sentencing Commission, Guidelines Manual (1991) parallels the statutory language and requires the base offense level to be determined based upon the weight of a “mixture or substance containing a detectable amount of” LSD.
  According to the Sentencing Commission, the LSD in an average dose weighs 0.05 milligrams; there are therefore 20,000 pure doses in a gram. The pure dose is such an infinitesimal amount that it must be sold to retail customers in a “carrier.” Pure LSD is dissolved in a solvent such as alcohol, and either the solution is sprayed on paper or gelatin, or paper is dipped in the solution. The solvent evaporates, leaving minute amounts of LSD trapped in the paper or gel. Then the paper or gel is cut into “one-dose” squares and sold by the dose. Users either swallow the squares, lick them until the drug is released, or drop them into a beverage, thereby releasing the drug. Although gelatin and paper are light, they weigh much more than the LSD. The ten sheets of blotter paper carrying the 1,000 doses sold by petitioners weighed 5.7 grams; the LSD by itself weighed only about 50 milligrams, not even close to the one gram necessary to trigger the 5-year mandatory minimum of §841(b)(1)(B)(v).
  Petitioners argue that § 841(b) should not require that the weight of the carrier be included when computing the appropriate sentence for LSD distribution, for the words “mixture or substance” are ambiguous and should not be construed to reach an illogical result. Because LSD is sold by dose, rather than by weight, the weight of the LSD carrier should not be included when determining a defendant’s sentence because it is irrelevant to culpability. They argue that including the weight of the carrier leads to anomalous results, viz: a major wholesaler caught with 19,999 doses of pure LSD would not be subject to the 5-year mandatory minimum sentence, while a minor pusher with 200 doses on blotter paper, or even one dose on a sugar cube, would be subject to the mandatory minimum sentence. Thus, they contend, the weight of the carrier should be excluded, the weight of the pure LSD should be determined, and that weight should be used to set the appropriate sentence.
  We think that petitioners’ reading of the statute — a reading that makes the penalty turn on the net weight of the drug rather than the gross weight of the carrier and drug together — is not a plausible one. The statute refers to a'“mixture or substance containing a detectable amount.” So long as it contains a detectable amount, the entire mixture or substance is to be weighed when calculating the sentence.
  This reading is confirmed by the structure of the statute. With respect to various drugs, including heroin, cocaine, and LSD, it provides for mandatory minimum sentences for crimes involving certain weights of a “mixture or substance containing a detectable amount” of the drugs. With respect to other drugs, however, namely phencyclidine (PCP) or methamphetamine, it provides for a mandatory minimum sentence based either on the weight of a mixture or substance containing a detectable amount of the drug, or on lower weights of pure PCP or methamphetamine. For example, § 841(b)(1)(A)(iv) provides for a mandatory 10-year minimum sentence for any person who distributes “100 grams or more of. . . PCP ... or 1 kilogram or more of a mixture or substance containing a detectable amount of. . . PCP. . . .” Thus, with respect to these two drugs, Congress clearly distinguished between the pure drug and a “mixture or substance containing a detectable amount of” the pure drug. But with respect to drugs such as LSD, which petitioners distributed, Congress declared that sentences should be based exclusively on the weight of the “mixture or substance.” Congress knew how to indicate that the weight of the pure drug was to be used to determine the sentence, and did not make that distinction with respect to LSD.
  Petitioners maintain that Congress could not have intended to include the weight of an LSD carrier for sentencing purposes because the carrier will constitute nearly all of the weight of the entire unit, and the sentence will, therefore, be based on the weight of the carrier, rather than the drug. The same point can be made about drugs like heroin and cocaine, however, and Congress clearly intended the dilutant, cutting agent, or carrier medium to be included in the weight of those drugs for sentencing purposes. Inactive ingredients are combined with pure heroin or cocaine, and the mixture is then sold to consumers as a heavily diluted form of the drug. In some cases, the concentration of the drug in the mixture is very low. E. g., United States v. Buggs, 904 F. 2d 1070 (CA7 1990) (1.2% heroin); United States v. Dorsey, 198 U. S. App. D. C. 313, 591 F. 2d 922 (1978) (2% heroin); United States v. Smith, 601 F. 2d 972 (CA8) (2.7% and 8.5% heroin), cert. denied, 444 U. S. 879 (1979). But, if the carrier is a “mixture or substance containing a detectable amount of the drug,” then under the language of the statute the weight of the mixture or substance, and not the weight of the pure drug, is controlling.
  The history of Congress’ attempts to control illegal drug distribution shows why Congress chose the course that it did with respect to sentencing. The Comprehensive Drug Abuse Prevention and Control Act of 1970, Pub. L. 91-513, 84 Stat. 1236, divided drugs by schedules according to potential for abuse. LSD was listed in schedule 1(c), which listed “any material, compound, mixture, or preparation, which contains any quantity of the following hallucinogenic substances,” including LSD. Pub. L. 91-513, § 202(c). That law did not link penalties to the quantity of the drug possessed; penalties instead depended upon whether the drug was classified as a narcotic or not.
  The Controlled Substances Penalties Amendments Act of 1984, which was a chapter of the Comprehensive Crime Control Act of 1984, Pub. L. 98-473, 98 Stat. 2068, first made punishment dependent upon the quantity of the controlled substance involved. The maximum sentence for distribution of five grams or more of LSD was set at 20 years. 21 U. S. C. § 841(b)(l)(A)(iv) (1982 ed., Supp. II). The 1984 amendments were intended “to provide a more rational penalty structure for the major drug trafficking offenses,” S. Rep. No. 98-225, p. 255 (1983), by eliminating sentencing disparaties caused by classifying drugs as narcotic and nonnarcotic. Id., at 256. Penalties were based instead upon the weight of the pure drug involved. See United States v. McGeehan, 824 F. 2d 677, 681 (CA8 1987), cert. denied, 484 U. S. 1061 (1988).
  The current penalties for LSD distribution originated in the Anti-Drug Abuse Act of 1986, Pub. L. 99-570, 100 Stat. 3207. Congress adopted a “market-oriented” approach to punishing drug trafficking, under which the total quantity of what is distributed, rather than the amount of pure drug involved, is used to determine the length of the sentence. H. R. Rep. No. 98-845, pt. 1, pp. 11-12, 17 (1986). To implement that principle, Congress set mandatory minimum sentences corresponding to the weight of a “mixture or substance containing a detectable amount of” the various controlled substances, including LSD. 21 U. S. C. §§ 841(b)(1) (A)(i)-(viii) and (B)(i)-(viii). It intended the penalties for drug trafficking to be graduated according to the weight of the drugs in whatever form they were found—cut or uncut, pure or impure, ready for wholesale or ready for distribution at the retail level. Congress did not want to punish retail traffickers less severely, even though they deal in smaller quantities of the pure drug, because such traffickers keep the street markets going. H. R. Rep. No. 99-845, supra, at pt. 1, p. 12.
  We think that the blotter paper used in this case, and blotter paper customarily used to distribute LSD, is a “mixture or substance containing a detectable amount” of LSD. In so holding, we confirm the unanimous conclusion of the Courts of Appeals that have addressed the issue. Neither the statute nor the Sentencing Guidelines define the terms “mixture” and “substance,” nor do they have any established common-law meaning. Those terms, therefore, must be given their ordinary meaning. See Moskal v. United States, 498 U. S. 103, 108 (1990). A “mixture” is defined to include “a portion of matter consisting of two or more components that do not bear a fixed proportion to one another and that however thoroughly commingled are regarded as retaining a separate existence.” Webster’s Third New International Dictionary 1449 (1986). A “mixture” may also consist of two substances blended together so that the particles of one are diffused among the particles of the other. 9 Oxford English Dictionary 921 (2d ed. 1989). LSD is applied to blotter paper in a solvent, which is absorbed into the paper and ultimately evaporates. After the solvent evaporates, the LSD is left behind in a form that can be said to “mix” with the paper. The LSD crystals are inside of the paper, so that they are commingled with it, but the LSD does not chemically combine with the paper. Thus, it retains a separate existence and can be released by dropping the paper into a liquid or by swallowing the paper itself. The LSD is diffused among the fibers of the paper. Like heroin or cocaine mixed with cutting agents, the LSD cannot be distinguished from the blotter paper, nor easily separated from it. Like cutting agents used with other drugs that are ingested, the blotter paper, gel, or sugar cube carrying LSD can be and often is ingested with the drug.
  Petitioners argue that the terms “mixture” or “substance” cannot be given their dictionary meaning because then the clause could be interpreted to include carriers like a glass vial or an automobile in which the drugs are being transported, thus making the phrase nonsensical. But such nonsense is not the necessary result of giving the term “mixture” its dictionary meaning. The term does not include LSD in a bot-tie, or LSD in a car, because the drug is easily distinguished from, and separated from, such a “container.” The drug is clearly not mixed with a glass vial or automobile; nor has the drug chemically bonded with the vial or car. It may be true that the weights of containers and packaging materials generally are not included in determining a sentence for drug distribution, but that is because those items are also clearly not mixed or otherwise combined with the drug.
  Petitioners argue that excluding the weight of the LSD carrier when determining a sentence is consistent with established principles of statutory construction. First, they argue that the rule of lenity requires an ambiguous statute of this type to be construed in favor of the defendant. Petitioners also argue that the statute should be construed to avoid a serious constitutional question and an interpretation of the statute that would require it to be struck down as violating due process.
  The rule of lenity, however, is not applicable unless there is a “grievous ambiguity or uncertainty in the language and structure of the Act,” Huddleston v. United States, 415 U. S. 814, 831 (1974), such that even after a court has “‘seize[d] every thing from which aid can be derived,’” it is still “left with an ambiguous statute.” United States v. Bass, 404 U. S. 336, 347 (1971) (quoting United States v. Fisher, 2 Cranch 358, 386 (1805)). “The rule [of lenity] comes into operation at the end of the process of construing what Congress has expressed, not at the beginning as an overriding consideration of being lenient to wrongdoers.” Callanan v. United States, 364 U. S. 587, 596 (1961). See also, e. g., Moskal v. United States, supra, at 107-108. The statutory language and structure indicate that the weight of a carrier should be included as a “mixture or substance containing a detectable amount” of LSD when determining the sentence for an LSD distributor. A straightforward reading of § 841(b) does not produce a result “so ‘absurd or glaringly unjust,’” United States v. Rodgers, 466 U. S. 475, 484 (1984) (citation omitted), as to raise a “reasonable doubt” about Congress’ intent. Moskal v. United States, supra, at 108. There is no reason to resort to the rule of lenity in these circumstances.
  Petitioners also argue that constructions which cast doubt on a statute’s constitutionality should be avoided, citing Public Citizen v. Department of Justice, 491 U. S. 440, 465-466 (1989). “ ‘[E]very reasonable construction must be resorted to, in order to save a statute from unconstitutionality,”’ Edward J. DeBartolo Corp. v. Florida Gulf Coast Building & Construction Trades Council, 485 U. S. 568, 575 (1988), but reading “mixture” to include blotter paper impregnated with LSD crystals is not only a reasonable construction of § 841(b), but it is one that does not raise “grave doubts” about the constitutionality of the provision. United States v. Jin Fuey Moy, 241 U. S. 394, 401 (1916). The canon of construction that a court should strive to interpret a statute in a way that will avoid an unconstitutional construction is useful in close cases, but it is “ ‘not a license for the judiciary to rewrite language enacted by the legislature.’” United States v. Monsanto, 491 U. S. 600, 611 (1989). Petitioners’ argument is unavailing here for the reasons we explain below.
  Petitioners argue that the due process of law guaranteed them by the Fifth Amendment is violated by determining the lengths of their sentences in accordance with the weight of the LSD “carrier,” a factor which they insist is arbitrary. They argue preliminarily that the right to be free from deprivations of liberty as a result of arbitrary sentences is fundamental, and therefore the statutory provision at issue may be upheld only if the Government has a compelling interest in the classification in question. But we have never subjected the criminal process to this sort of truncated analysis, and we decline to do so now. Every person has a fundamental right to liberty in the sense that the Government may not punish him unless and until it proves his guilt beyond a reasonable doubt at a criminal trial conducted in accordance with the relevant constitutional guarantees. Bell v. Wolfish, 441 U. S. 520, 535, 536, and n. 16 (1979). But a person who has been so convicted is eligible for, and the court may impose, whatever punishment is authorized by statute for his offense, so long as that penalty is not cruel and unusual, McMillan v. Pennsylvania, 477 U. S. 79, 92, n. 8 (1986); Meachum v. Fano, 427 U. S. 215, 224 (1976), and so long as the penalty is not based on an arbitrary distinction that would violate the Due Process Clause of the Fifth Amendment. In this context, as we noted in Jones v. United States, 463 U. S. 354, 362, n. 10 (1983), an argument based on equal protection essentially duplicates an argument based on due process.
  We find that Congress had a rational basis for its choice of penalties for LSD distribution. The penalty scheme set out in the Anti-Drug Abuse Act of 1986 is intended to punish severely large-volume drug traffickers at any level. H. R. Rep. No. 99-845, pt. 1, at 12, 17. It assigns more severe penalties to the distribution of larger quantities of drugs. By measuring the quantity of the drugs according to the “street weight” of the drugs in the diluted form in which they are sold, rather than according to the net weight of the active component, the statute and the Sentencing Guidelines increase the penalty for persons who possess large quantities of drugs, regardless of their purity. That is a rational sentencing scheme.
  This is as true with respect to LSD as it is with respect to other drugs. Although LSD is not sold by weight, but by dose, and a carrier medium is not, strictly speaking, used to “dilute” the drug, that medium is used to facilitate the distribution of the drug. Blotter paper makes LSD easier to transport, store, conceal, and sell. It is a tool of the trade for those who traffic in the drug, and therefore it was rational for Congress to set penalties based on this chosen tool. Congress was also justified in seeking to avoid arguments about the accurate weight of pure drugs which might have been extracted from blotter paper had it chosen to calibrate sentences according to that weight.
  Petitioners do not claim that the sentencing scheme at issue here has actually produced an arbitrary array of sentences, nor did their motions in District Court contain any proof of actual disparities in sentencing. Rather, they challenge the Act on its face on the ground that it will inevitably lead to arbitrary punishments. While hypothetical cases can be imagined involving very heavy carriers and very little LSD, those cases are of no import in considering a claim by persons such as petitioners, who used a standard LSD carrier. Blotter paper seems to be the carrier of choice, and the vast majority of cases will therefore do exactly what the sentencing scheme was designed to do — punish more heavily those who deal in larger amounts of drugs.
  Petitioners argue that those selling different numbers of doses, and, therefore, with different degrees of culpability, will be subject to the same minimum sentence because of choosing different carriers. The same objection could be made to a statute that imposed a fixed sentence for distributing any quantity of LSD, in any form, with any carrier. Such a sentencing scheme — not considering individual degrees of culpability — would clearly be constitutional. Congress has the power to define criminal punishments without giving the courts any sentencing discretion. Ex parte United States, 242 U. S. 27 (1916). Determinate sentences were found in this country’s penal codes from its inception, see United States v. Grayson, 438 U. S. 41, 45-46 (1978), and some have remained until the present. See, e. g., 18 U. S. C. §1111 (mandatory life imprisonment under federal first-degree-murder statute); 21 U. S. C. § 848(b) (mandatory life imprisonment for violation of drug “super-kingpin” statute); 18 U. S. C. §2114 (1982 ed.) (flat 25-year sentence for armed robbery of a postal carrier) (upheld against due process challenge in United States v. Smith, 602 F. 2d 834 (CA8), cert. denied, 444 U. S. 902 (1979), and Smith v. United States, 284 F. 2d 789, 791 (CA5 1960)). A sentencing scheme providing for “individualized sentences rests not on constitutional commands, but on public policy enacted into statutes.” Lockett v. Ohio, 438 U. S. 586, 604-605 (1978) (plurality opinion). See also Mistretta v. United States, 488 U. S. 361, 364 (1989). That distributors of varying degrees of culpability might be subject to the same sentence does not mean that the penalty system for LSD distribution is unconstitutional.
  We likewise hold that the statute is not unconstitutionally vague. First Amendment freedoms are not infringed by §841, so the vagueness claim must be evaluated as the statute is applied to the facts of this case. United States v. Powell, 423 U. S. 87, 92 (1975). The fact that there may be plausible arguments against describing blotter paper impregnated with LSD as a “mixture or substance” containing LSD does not mean that the statute is vague. This is particularly so since whatever debate there is would center around the appropriate sentence and not the criminality of the conduct. We upheld the defendant’s conviction in United States v. Rodgers, 466 U. S. 475 (1984), even though the Court of Appeals for the Circuit in which the defendant had resided had construed the statute as not applying to one in his position. Here, on the contrary, all of the Courts of Appeals that have decided the issue, and all except one District Court, United States v. Healy, 729 F. Supp. 140 (DC 1990), have held that the weight of the carrier medium must be included in determining the appropriate sentence.
  We hold that the statute requires the weight of the carrier medium to be included when determining the appropriate sentence for trafficking in LSD, and that this construction is neither a violation of due process nor unconstitutionally vague. Accordingly, the judgment of the Court of Appeals is
  Affirmed.
  Chapman was sentenced to 96 months; Schoenecker was sentenced to 63 months; and Brumm was sentenced to 60 months’ imprisonment. Brief for Petitioners 4.
  Likewise, under the Sentencing Guidelines, those selling the same number of doses would be subject to widely varying sentences depending upon which carrier medium was used. For example, those selling 100 doses would receive the following disparate sentences:
  Brief for Petitioners 11 (footnotes omitted).
  Even among dealers using blotter paper, the sentences can vary because the weight of the blotter paper varies from dealer to dealer. Petitioners’ blotter paper, containing 1,000 doses of LSD, weighed 5.7 grams, or 5.7 milligrams per dose. In United States v. Rose, 881 F. 2d 386, 387 (CA7 1989), 472 doses on blotter paper weighed 7.3 grams, or 15.4 milligrams per dose. In United States v. Elrod, 898 F. 2d 60 (CA6 1990), 1,990 doses on blotter paper weighed 11 grams, or 5.5 milligrams per dose. In United States v. Healy, 729 F. Supp. 140, 141 (DC 1990), 5,000 doses on blotter paper weighed 44.133 grams, or 8.8 milligrams per dose.
  United States v. Larsen, 904 F. 2d 562 (CA10 1990); United States v. Elrod, 898 F. 2d 60 (CA6), cert. denied, 498 U. S. 835 (1990); United States v. Bishop, 894 F. 2d 981, 985-987 (CA8 1990); United States v. Daly, 883 F. 2d 313, 316-318 (CA4 1989), cert. denied, 498 U. S. 1116 (1990); United States v. Rose, 881 F. 2d 386 (CAT 1989); United States v. Taylor, 868 F. 2d 125, 127-128 (CA5 1989).
  Petitioners point to the views of some Members of Congress that the use of the phrase “mixture or substance containing a detectable amount of LSD” was less than precise. These views were manifested by the introduction of bills in the Senate that would have excluded LSD carrier mediums from the “mixture or substance” clause. Neither of the bills was enacted into law, and it is questionable whether they even amount to subsequent legislative history—itself an unreliable guide to legislative intent. See Pierce v. Underwood, 487 U. S. 552, 566-567 (1988); Quern v. Mandley, 436 U. S. 725, 736, n. 10 (1978).
  Every Court of Appeals to have addressed the issue has held that this sentencing scheme is rational. See United States v. Mendes, 912 F. 2d 434, 438-439 (CA10 1990); see United States v. Murphy, 899 F. 2d 714, 717 (CA8 1990); United States v. Bishop, 894 F. 2d, at 986-987; United States v. Holmes, 838 F. 2d 1175, 1177-1178 (CA11), cert. denied, 486 U. S. 1058 (1988); United States v. Klein, 860 F. 2d 1489, 1501 (CA9 1988); United States v. Hoyt, 879 F. 2d 505, 512 (CA9 1989); United States v. Savinovich, 845 F. 2d 834, 839 (CA9), cert. denied, 488 U. S. 943 (1988); United States v. Ramos, 861 F. 2d 228, 231-232 (CA9 1988).
  We note that distributors of LSD make their own choice of carrier and could act to minimize their potential sentences. As it is, almost all distributors choose blotter paper, rather than the heavier and bulkier sugar cubes.