Testing and confidence interval construction for a parameter are achie
ved by constructing a pivotal. In this paper we study construction of
approximate pivotals from recapture models where capture probabilities
possibly vary from occasion to occasion. We compare the asymptotic st
andard normality of various pivotals including analogues of the classi
cal maximum likelihood/Wald, score and likelihood ratio statistics. So
me bias adjustments are developed and indicate that the score pivotal
has smaller bias than the pivotal of Chao (1989). The score and likeli
hood ratio pivotals both provide intervals with accurate two-sided cov
erage, but one-sided coverage accuracy varies. Chao's pivotal appears
to be slightly conservative but is the simplest to compute. Classical
pivotals based directly on the estimator are inadequate.