Most research on the creative process has focused on idea generation, and the prevalence and influence of many other creative subprocesses remain poorly understood. To clarify different subprocesses' respective roles in creative work, this study investigated their frequencies and associations with creativity-related personal characteristics and product creativity. Undergraduate students (n = 266) articulated their creative thought processes via the think aloud method while completing an open-ended drawing task and completed questionnaires assessing creativity-relevant personal characteristics. Drawings were rated for creativity by quasi-expert judges. Transcripts were coded using an a priori coding scheme informed by models of the creative process, including generation (14%), elaboration (26%), association (9%), selection (4%), evaluation (13%), anchoring (13%), metacognition (7%), and filler (14%). Subprocess frequencies correlated minimally with measures of personal characteristics, although several significant, albeit weak, relationships emerged. A hierarchical regression analysis indicated that the best predictors of drawing creativity were aesthetic fluency, the frequency of anchoring, time spent on task, and, marginally, the frequency of generation. Together, these results provide insight into how relevant personal characteristics and subprocess engagement contribute to drawing creativity and highlight the particular importance of anchoring, which involves monitoring and refining task-related goals and constraints, throughout the creative process.