It has been argued that environmental variability favors variation in offspring size. We have examined theoretically the effects of three types of environmental heterogeneity on parental investment: spatial variation, spatial variation with density-dependent offspring fitness, and temporal variability. We concluded that environmental heterogeneity rarely favors the production of variable offspring. With spatial heterogeneity and no density dependence in fitness, a single offspring size is always optimal. Variable offspring may be favored if density-dependent fitness loss to offspring is large and if parents can control the dispersal of offspring to the appropriate habitats. If environments vary temporally, the predicted optimal parental investment strategy depends on the measure of fitness used. If the arithmetic mean of fitness is used, a single offspring size is always favored. Variable offspring sizes are sometimes selected if fitness is measured by the arithmetic mean discounted for the variance or by the geometric mean. Our results differ from those of R. Kaplan and Cooper (1984) because of differences in our assumptions about the relationship among offspring fitness, offspring size, and environmental quality. Although a single offspring size is often the optimal parental investment strategy according to our models, considerable variation in the size of eggs/seeds/young has been found in animals and plants. We suggest that an organism's ability to control investment in offspring precisely and to reduce the variation in offspring size may be constrained by such factors as pleiotropy and positional, temporal, and environmental effects during offspring development. We suggest that animals are more likely to exhibit adaptive offspring size variation than plants because of their greater ability to assess environmental conditions and to disperse offspring to appropriate habitats.