While there is broad consensus that non-insight problems are typically solved through conscious, stepwise processes, the mechanisms underlying insight problem solving remain under debate. According to the view, insight relies on an unconscious restructuring that is susceptible to verbal overshadowing. In contrast, the approach maintains that insight and non-insight solutions both emerge via similar, conscious procedures that should be unaffected by verbalization. A third, challenging, perspective, the approach, claims that the insight problem-solving process is not only unconscious but also analytic, instead of being merely associative. Actually, this process requires cognitive resources also works at an unconscious layer, suggesting that it can be disrupted by forced verbalization, which demands great cognitive effort. Therefore, according to this approach, being asked to verbalize the simultaneous processing of insight problem solving would hampers restructuring. To disentangle these positions, we compared participants' performances on an insight problem and a non-insight problem under either concurrent verbalization or silent conditions. Our results show that verbalization significantly hampered insight problem solving, yet dramatically aided non-insight performance. Overall, our results provide evidence supporting the role of unconscious analytic processes in the resolution of insight problems, in contrast with the stepwise, conscious procedure used for the resolution of non-insight problems.