In most free-recall experiments, participants are given a preset amount of time to search memory. Recently, several studies have examined retrieval in an open-interval design in which the participant, not the experimenter, determines when to terminate memory search. The present study performs the first direct comparison between participant-terminated and experimenter-terminated retrieval. No difference was found in the number of items retrieved from memory; however, inter-retrieval times (IRTs) did differ, such that the participant-terminated paradigm did not show the hyperbolic function typically found when using the experimenter-determined, closed-interval design. We were able to account for this result by equipping a simple relative sampling model with a memory search stopping rule that assumes that giving participants a pre-set retrieval interval causes them to search longer (and tolerate more search failures) than they would in the open-interval design.