Stimulus-independent thoughts (SITs) are streams of thoughts and images unrelated to immediate sensory input. Four experiments examined the contribution of aspects of working memory to production of SITs. In Experiments 1 and 2, interventions that were targeted on, respectively, phonological and visuospatial components of working memory both interfered with production of SITs, but there was evidence that these tasks also made demands on central executive resources. Experiments 3 and 4 specifically examined the hypothesis that production of SITs and control of nonproceduralized tasks both depend on central executive resources, and so should show mutual interference. In Experiment 3, prior practice on pursuit rotor and memory tasks reduced the interference with SITs from concurrent task performance. In Experiment 4, randomness within a task involving random-number generation was less when SITs were being produced concurrently than it was when they were not. The results suggest that production of SITs depends on central executive resources.