A model of the rates of discovery of positives and true and false negatives for the cases of single and double screening determinations (especially cervical cancer) was developed for a special case. In this model positives were defined as screening outcomes resulting in some further action involving further cost--diagnostic or treatment--whether justified by later verification or not. For Pap smears the literature shows a substantial improvement in number of positives discovered by using double smears. Using this model, prevalence of positives can be estimated with one screening using double smears on a given cohort and prevalence and incidence in two screenings. Sources of data to estimate benefit/cost improvements by use of double smears are being explored.