The take of Nearctic songbirds for the caged-bird trade is an important cultural and economic activity in Mexico, but its sustainability has been questioned. We relied on the theta-logistic population model to explore options for setting allowable levels of take for 11 species of passerines that were subject to legal take in Mexico in 2010. Because estimates of population size necessary for making periodic adjustments to levels of take are not routinely available, we examined the conditions under which a constant level of take might contribute to population depletion (i.e., a population below its level of maximum net productivity). The chance of depleting a population is highest when levels of take are based on population sizes that happen to be much lower or higher than the level of maximum net productivity, when environmental variation is relatively high and serially correlated, and when the interval between estimation of population size is relatively long (≥5 years). To estimate demographic rates of songbirds involved in the Mexican trade we relied on published information and allometric relationships to develop probability distributions for key rates, and then sampled from those distributions to characterize the uncertainty in potential levels of take. Estimates of the intrinsic rate of growth (r) were highly variable, but median estimates were consistent with those expected for relatively short-lived, highly fecund species. Allowing for the possibility of nonlinear density dependence generally resulted in allowable levels of take that were lower than would have been the case under an assumption of linearity. Levels of take authorized by the Mexican government in 2010 for the 11 species we examined were small in comparison to relatively conservative allowable levels of take (i.e., those intended to achieve 50% of maximum sustainable yield). However, the actual levels of take in Mexico are unknown and almost certainly exceed the authorized take. Also, the take of Nearctic songbirds in other Latin American and Caribbean countries ultimately must be considered in assessing population-level impacts.