Differences among patients can moderate the impact of evidence-based treatments (i.e., heterogeneity of treatment effects), leading patients to get more or less benefit. The Learning About My Pain (LAMP) study was a randomized comparative effectiveness trial of 10-week literacy-adapted group cognitive-behavioral therapy for chronic pain (CBT) vs. pain psychoeducation groups (EDU) vs. usual medical care (UC). We examined potential sociodemographic and cognitive moderators of treatment effect among participants with post-treatment assessments (N = 241). Analyses were conducted using moderation in the PROCESS macro in SPSS and significant interactions were explored further. Education and primary literacy moderated the difference between CBT and EDU on pain intensity; primary literacy, health literacy, and working memory moderated the difference between CBT and EDU on pain interference. Analyses revealed few significant moderation effects relative to UC. No moderators were identified for depression. Neither sex nor minority status moderated any differences between groups. Patients with lower education, literacy, and working memory gained more benefit from CBT than EDU. When provided sufficient guidance and structure in a way that is meaningfully adapted, highly disadvantaged patients achieved as much benefit as less disadvantaged patients, suggesting that the literacy-adapted CBT more successfully met the needs of this population. Trial registration: clinicaltrials.gov identifier NCT01967342 Perspective: This article presents findings related to heterogeneity of treatment effects for simplified group psychosocial treatments for chronic pain. The results suggest that educationally, cognitively, or literacy-disadvantaged patients benefit most from the more structured approach of literacy-adapted cognitive-behavioral therapy rather than psychoeducation, whereas less disadvantaged patients benefit from either treatment.