The tumor suppressor p53 slides along DNA while searching for its cognate site. Central to this process is the basic C-terminal domain, whose regulatory role and its coordination with the core DNA-binding domain is highly debated. Here we use single-molecule techniques to characterize the search process and disentangle the roles played by these two DNA-binding domains in the search process. We demonstrate that the C-terminal domain is capable of rapid translocation, while the core domain is unable to slide and instead hops along DNA. These findings are integrated into a model, in which the C-terminal domain mediates fast sliding of p53, while the core domain samples DNA by frequent dissociation and reassociation, allowing for rapid scanning of long DNA regions. The model further proposes how modifications of the C-terminal domain can activate "latent" p53 and reconciles seemingly contradictory data on the action of different domains and their coordination.