In response to DNA damage during S phase, cells slow DNA replication. This slowing is orchestrated by the intra-S checkpoint and involves inhibition of origin firing and reduction of replication fork speed. Slowing of replication allows for tolerance of DNA damage and suppresses genomic instability. Although the mechanisms of origin inhibition by the intra-S checkpoint are understood, major questions remain about how the checkpoint regulates replication forks: Does the checkpoint regulate the rate of fork progression? Does the checkpoint affect all forks, or only those encountering damage? Does the checkpoint facilitate the replication of polymerase-blocking lesions? To address these questions, we have analyzed the checkpoint in the fission yeast Schizosaccharomyces pombe using a single-molecule DNA combing assay, which allows us to unambiguously separate the contribution of origin and fork regulation towards replication slowing, and allows us to investigate the behavior of individual forks. Moreover, we have interrogated the role of forks interacting with individual sites of damage by using three damaging agents—MMS, 4NQO and bleomycin—that cause similar levels of replication slowing with very different frequency of DNA lesions. We find that the checkpoint slows replication by inhibiting origin firing, but not by decreasing fork rates. However, the checkpoint appears to facilitate replication of damaged templates, allowing forks to more quickly pass lesions. Finally, using a novel analytic approach, we rigorously identify fork stalling events in our combing data and show that they play a previously unappreciated role in shaping replication kinetics in response to DNA damage.