It is a consequence of the likelihood principle that identical likelihood functions imply identical inferences. If the rule by which sample size is determined—the stopping rule—is reflected in the likelihood function, as it should be, apparently identical likelihood functions (without allowance for stopping rule) may in fact be different. This can happen if the stopping rules are informative. If the stopping rule is informative, the analysis must take the rule into account, and additional information may be recovered by so doing. Examples of informative stopping rules are given for two simple problems in estimation of the size of finite populations, and an illustrative Bayesian analysis is shown in each problem. Other informative stopping rules are briefly discussed.