We develop a novel method of estimating population size from imperfectly detected counts of individuals and a separate estimate of detection probability. Observed counts are separated into classes within which detection probability is assumed constant. Within a detection class, counts are modeled as a single binomial observation X with success probability p where the goal is to estimate index N. We use a Horvitz–Thompson‐like estimator for N and account for uncertainty in both sample data and estimated success probability via a parametric bootstrap. Unlike capture–recapture methods, our model does not require repeated sampling of the population. Our method is able to achieve good results, even with small X. We show in a factorial simulation study that the median of the bootstrapped sample has small bias relative to N and that coverage probabilities of confidence intervals for N are near nominal under a wide array of scenarios. Our methodology begins to break down when P(X=0)>0.1 but is still capable of obtaining reasonable confidence coverage. We illustrate the proposed technique by estimating (1) the size of a moose population in Alaska and (2) the number of bat fatalities at a wind power facility, both from samples with imperfect detection probabilities, estimated independently.