Analyses of effects of mutants on many traits have enabled estimates to be obtained of the magnitude of pleiotropy, and in reviews of such data others have concluded that the degree of pleiotropy is highly restricted, with implications on the evolvability of complex organisms. We show that these conclusions are highly dependent on statistical assumptions, for example significance levels. We analyze models with pleiotropic effects on all traits at all loci but by variable amounts, considering distributions of numbers of traits declared significant, overall pleiotropic effects, and extent of apparent modularity of effects. We demonstrate that these highly pleiotropic models can give results similar to those obtained in analyses of experimental data and that conclusions on limits to evolvability through pleiotropy are not robust.