The inefficient translocation of proteins across biological membranes limits their application as potential therapeutics and research tools. In many cases, the translocation of a protein involves two discrete steps: uptake into the endocytic pathway and endosomal escape. Certain charged or amphiphilic molecules can achieve high protein uptake, but few are capable of efficient endosomal escape. One exception to this rule is ZF5.3, a mini-protein that exploits elements of the natural endosomal maturation machinery to translocate across endosomal membranes. Although some ZF5.3-protein conjugates are delivered efficiently to the cytosol or nucleus, overall delivery efficiency varies widely for different cargoes with no obvious design rules. Here we show that delivery efficiency depends on the ability of the cargo to unfold. Using fluorescence correlation spectroscopy, a single-molecule technique that precisely measures intracytosolic protein concentration, we show that regardless of size and pI, low-Tm cargoes of ZF5.3 (including intrinsically disordered domains) bias endosomal escape toward a high-efficiency pathway that requires the homotypic fusion and protein sorting (HOPS) complex. Small protein domains are delivered with moderate efficiency through the same HOPS portal, even if the Tm is high. These findings imply a novel pathway out of endosomes that is exploited by ZF5.3 and provide clear guidance for the selection or design of optimally deliverable therapeutic cargo.