The effective population size (Ne), and the ratio between Ne and census population size (N) are often used as measures of population viability. We show that using the harmonic mean of population sizes over time – a common proxy for Ne– has some important evolutionary consequences and implications for conservation management. This stems from the fact that there is no unambiguous relationship between the arithmetic and harmonic means for populations fluctuating in size. As long as the variance of population size increases moderately with increasing arithmetic mean population size, the harmonic mean also increases. However, if the variance of population size increases more rapidly, which existing data often suggest, then the harmonic mean may actually decrease with increasing arithmetic mean. Thus maximizing N may not maximize Ne, but could instead lower the adaptive potential and hence limit the evolutionary response to environmental change. Large census size has the clear advantage of lowering demographic stochasticity, and hence extinction risk, and under certain conditions large census size also minimizes the loss of genetic variation. Consequently, maximising census size has served as a useful dogma in ecology, genetics and conservation. Nonetheless, due to the intricate relationships among Ne, population viability and the properties of population fluctuations, we suggest that this dogma should be taken only as a rule of thumb.