: Many HIV prevalence surveys are plagued by the problem that a sizeable number of surveyed individuals do not consent to contribute blood samples for testing. One can ignore this problem, as is often done, but the resultant bias can be of sufficient magnitude to invalidate the results of the survey, especially if the number of non-responders is high and the reason for refusing to participate is related to the individual's HIV status. One reason for refusing to participate may be for reasons of privacy. For those individuals, we suggest offering the option of being tested in a pool. This form of testing is less certain than individual testing, but, if it convinces more people to submit to testing, it should reduce the potential for bias and give a cleaner answer to the question of prevalence. This paper explores the logistics of implementing a combined individual and pooled testing approach and evaluates the analytical advantages to such a combined testing strategy. We quantify improvements in a prevalence estimator based on this combined testing strategy, relative to an individual testing only approach and a pooled testing only approach. Minimizing non-response is key for reducing bias, and, if pooled testing assuages privacy concerns, offering a pooled testing strategy has the potential to substantially improve HIV prevalence estimates.