How enhancers activate their distal target promoters remains incompletely understood. Here we dissect how CTCF-mediated loops facilitate and restrict such regulatory interactions. Using an allelic series of mouse mutants, we show that CTCF is neither required for the interaction of the Sox2 gene with distal enhancers, nor for its expression. Insertion of various combinations of CTCF motifs, between Sox2 and its distal enhancers, generated boundaries with varying degrees of insulation that directly correlated with reduced transcriptional output. However, in both epiblast and neural tissues, enhancer contacts and transcriptional induction could not be fully abolished, and insertions failed to disrupt implantation and neurogenesis. In contrast, Sox2 expression was undetectable in the anterior foregut of mutants carrying the strongest boundaries, and these animals fully phenocopied loss of SOX2 in this tissue. We propose that enhancer clusters with a high density of regulatory activity can better overcome physical barriers to maintain faithful gene expression and phenotypic robustness.