Individuals encounter problems daily wherein varying numbers of constraints require delimitation of memory to target goal-satisfying information. Multiply-constrained problems, such as the compound remote associates, are commonly used to study this type of problem solving. Since their development, multiply-constrained problems have been theoretically and empirically related to creative thinking, analytical problem solving, insight problem solving, and a multitude of other cognitive abilities. In the present study, we empirically evaluated the range of cognitive abilities previously associated with multiply-constrained problem solving to assess common versus unique predictive variance (i.e., working memory, attention control, episodic and semantic memory, and fluid and crystallized intelligence). Additionally, we sought to determine whether problem-solving ability and self-reported strategy adoption (analytical or insightful) were task specific or task general through the use of novel multiply-constrained problem-solving tasks (TriBond and Location Bond). Performance across these tasks was shown to be domain general, solutions derived through insightful strategies were more often correct than those derived through analytical strategies, and crystallized intelligence was the sole cognitive ability that provided unique predictive value after accounting for all other abilities.