Cell-free (CF) multiple-input multiple-output (MIMO) systems generally employ linear precoding techniques to mitigate the effects of multiuser interference. However, the power loss, efficiency, and precoding accuracy of linear precoders are usually improved by replacing them with nonlinear precoders that employ perturbation and modulo operation. In this work, we propose nonlinear user-centric precoders for CF MIMO, wherein different clusters of access points (APs) serve different users in CF multiple-antenna networks. Each cluster of APs is selected based on large-scale fading coefficients. The clustering procedure results in a sparse nonlinear precoder. We further devise a reduced-dimension nonlinear precoder, where clusters of users are created to reduce the complexity of the nonlinear precoder, the amount of required signaling, and the number of users. Numerical experiments show that the proposed nonlinear techniques for CF systems lead to an enhanced performance when compared to their linear counterparts.