Suicide attempts (SA) are increasing in the United States, especially in veterans. Discovering individual cognitive features of the subset of suicide ideators who attempt suicide is critical. Cognitive theories attribute SA to facile schema-based negative interpretations of environmental events. Over-general autobiographical memory and facile solutions in problem solving tasks in SA survivors suggest that aversion to expending cognitive effort may be a neurobehavioral marker of SA risk. In veterans receiving care for mood disorder, we compared cognitive effort discounting and evidence-gathering in a beads task between veterans with (SAHx+; n = 26) versus without (SAHx-; n = 22) a history of SA. Groups did not differ in depressed mood or in a proxy metric of premorbid intelligence. Compared to SAHx- participants, SAHx+ participants self-reported significantly more severe cognitive problems in most domains, and also eschewed choice to earn higher monetary reward if earning it required a slightly increased working memory (WM) demand relative to an easy WM task. There was no group difference, however, in extent of evidence-gathering before declaring a conclusion in a beads task. These preliminary data suggest that aversion to expenditure of cognitive effort, potentially as a component of cognitive difficulties, may be a marker for SA risk.