Recent studies have shown that the effects of irrelevant spatial stimulus-response (S-R) correspondence (i.e., the Simon effect) occur only after trials in which the stimulus and response locations corresponded. This has been attributed to the gating of irrelevant information or the suppression of an automatic S-R route after experiencing a noncorresponding trial—a challenge to the widespread assumption of direct, intentionally unmediated links between spatial stimulus and response codes. However, trial sequences in a Simon task are likely to produce effects of stimulus- and response-feature integration that may mimic the sequential dependencies of Simon effects. Four experiments confirmed that Simon effects are eliminated if the preceding trial involved a noncorresponding S-R pair. However, this was true even when the preceding response did not depend on the preceding stimulus or if the preceding trial required no response at all. These findings rule out gating/suppression accounts that attribute sequential dependencies to response selection difficulties. Moreover, they are consistent with a feature-integration approach and demonstrate that accounting for the sequential dependencies of Simon effects does not require the assumption of information gating or response suppression.