The cooling of baryons in the centers of dark matter halos leads to a more concentrated dark matter distribution. This effect has traditionally been calculated using the model of adiabatic contraction, which assumes spherical symmetry, while in hierarchical formation scenarios halos grow via multiple violent mergers. We test the adiabatic contraction model in high-resolution cosmological simulations and find that the dissipation of gas indeed increases the density of dark matter and steepens its radial profile compared to the case without cooling. Although the standard model systematically overpredicts the increase of dark matter density, a simple modification of the assumed invariant from M(r)r to $M(\bar{r})r$, where $\bar{r}$ is the orbit-averaged particle position, reproduces the simulated profiles within 10%.