It is possible to control the sample size by multiplying the acceptance probability with a constant formula_24. For a larger sample size, pick formula_25 and adjust the acceptance probability to formula_26. For a smaller sample size, the same strategy applies. In cases where the number of samples desired is precise, a convenient alternative method is to uniformly downsample from a larger subsample selected by local case-control sampling. The algorithm has the following properties. When the pilot is consistent, the estimates using the samples from local case-control sampling is consistent even under model misspecification. If the model is correct then the algorithm has exactly twice the asymptotic variance of logistic regression on the full data set. For a larger sample size with formula_25, the factor 2 is improved to formula_28.