A number of methods exist for estimating the size of animal populations. All methods generate an uncertain estimate of population size, and have different properties, which can be taken into account when designing regulation. We consider hunting regulation when the population size is uncertain and when the self-reported bag is used to estimate the population size. The properties of a population tax and a tax on self-reported bag are analyzed and we begin by considering a baseline situation with full certainty and no use of self-reporting for population size estimation. Here individual hunters self-report a bag on zero and a population tax alone can secure an optimum. Next we show that when facing uncertain population size, a risk-averse hunter will self-report part of the bag to reduce the uncertain population tax payment, making both tax instruments necessary for reaching an optimum. Finally, when self-reported bag is used to estimate population size, we also show that it is optimal for hunters to report a part of the bag and both instruments are again necessary for reaching an optimum.