Pleiotropic effects among quantitative characters are believed to be extensive and universal, although their actual amount and pattern remains to be determined. Theoretical studies have shown that pleiotropic effects can influence the dynamics of a character under stabilizing selection and mutation through genetic correlations as well as hidden pleiotropic effects. It is further known that pleiotropic effects on fitness can cause an apparent stabilizing selection for an otherwise neutral character. The response to directional selection also depends on genetic correlations to other characters via correlated selection responses and deleterious side effects. In this paper we analyze a class of models for the adaptation of complex organisms based on three assumptions: (1) pleiotropic effects among characters are extensive, even in the absence of genetic correlations (hidden pleiotropic effects); (2) directional selection only acts on one or a small number of characters simultaneously (mosaic evolution); (3) the remaining characters are either neutral or under stabilizing selection. We show that the response to directed natural selection is strongly influenced by hidden pleiotropic effects on a second uncorrelated character which is under stabilizing selection. The hidden pleiotropic effects are inducing apparent stabilizing selection which interacts with the directional selection acting on the first character. The apparent stabilizing selection is mediated through the dynamics of the genetic variance associated with a change in the mean genotypic value. The result can be either inhibitory or accelerating, depending on the frequency of the alleles. The inhibitory effect can even completely prevent a response to directional selection if apparent stabilizing selection is strong compared to directional selection. In finite populations, the asymptotic rate of evolution is also influenced by hidden pleiotropic effects. This is mostly caused by a reduction of the asymptotic genetic variance maintained by mutation under sustained directional selection. It is concluded that hidden pleiotropic effects lead to adaptive inertia even in the absence of genetic correlations.