The computer simulation results of Hilborn et al. (R. Hilborn, J. A. Redfield, and C. J. Krebs. 1976. Can. J. Zool. 54: 1019–1024) regarding the bias of the 'minimum number alive' estimator of population size are shown to be in error. Minimum numbers alive are approximately twice as biased as estimated by these authors: for five species of Microtus the negative bias is estimated as 24–45% instead of 10–18%. 'Minimum number alive' differs from the Jolly–Seber population estimate in being particularly sensitive to mean trappability when the coefficient of variation of trappability is constant. Both population estimators are highly sensitive to reduced trappability of unmarked animals. The Jolly–Seber estimator remains the method of choice for open populations, especially if the coefficient of variation in trappability can be minimized.