In everyday life, we mainly solve problems with a conscious solution search (non-insight). However, sometimes a perplexing problem is resolved by a quantum leap in understanding. This phenomenon is known as the Aha! experience (insight). Although insight has a distinct phenomenological and behavioral signature, its driving mechanism remains debated. Weisberg (2015) proposed an integrated theory of insight arguing that insight, like non-insight, mainly depends on conscious, cognitive operations with restructuring as a distinguishing feature of insight. However, only if those operations lead to an impasse, insight is achieved through unconscious processes. We assessed some of the premises of this theory by asking participants (N = 42) to solve 70 word puzzles (CRAT) that can either be solved with insight or non-insight. For each puzzle, participants indicated word puzzle difficulty, solution confidence, solution suddenness, and the experiences of impasse and restructuring. As expected, participants reported higher suddenness of and confidence in insight solutions than non-insightful ones. Surprisingly, we could not corroborate the otherwise consistently reported higher solution accuracy and faster solution speed for insight. Crucially, as suggested by the integrated theory of insight, impasse was not a prerequisite for insight to occur. Although restructuring, indeed, preceded insight solutions more often, it seemed a more general problem-solving skill also applied for non-insight solutions. Moreover, early on, participants reported an increased experience of problem difficulty for puzzles later solved with insight. This ability to report on the solution search of insight demonstrates that, as proposed by the theory, insight involves conscious, cognitive operations.