Pooled CRISPR screens are a powerful tool for assessments of gene function. However, conventional analysis is based exclusively on the relative abundance of integrated single guide RNAs (sgRNAs) between populations, which does not discern distinct phenotypes and editing outcomes generated by identical sgRNAs. Here we present CRISPR-UMI, a single-cell lineage-tracing methodology for pooled screening to account for cell heterogeneity. We generated complex sgRNA libraries with unique molecular identifiers (UMIs) that allowed for screening of clonally expanded, individually tagged cells. A proof-of-principle CRISPR-UMI negative-selection screen provided increased sensitivity and robustness compared with conventional analysis by accounting for underlying cellular and editing-outcome heterogeneity and detection of outlier clones. Furthermore, a CRISPR-UMI positive-selection screen uncovered new roadblocks in reprogramming mouse embryonic fibroblasts as pluripotent stem cells, distinguishing reprogramming frequency and speed (i.e., effect size and probability). CRISPR-UMI boosts the predictive power, sensitivity, and information content of pooled CRISPR screens.