The bacterial chaperonin GroEL/GroES assists folding of a broad spectrum of denatured and misfolded proteins. Here, we explore the limits of this remarkable promiscuity by mapping two denatured proteins with very different conformational properties, rhodanese and cyclophilin A, during binding and encapsulation by GroEL/GroES with single-molecule spectroscopy, microfluidic mixing, and ensemble kinetics. We find that both proteins bind to GroEL with high affinity in a reaction involving substantial conformational adaptation. However, whereas the compact denatured state of rhodanese is encapsulated efficiently upon addition of GroES and ATP, the more expanded and unstructured denatured cyclophilin A is not encapsulated but is expelled into solution. The origin of this surprising disparity is the weaker interactions of cyclophilin A with a transiently formed GroEL-GroES complex, which may serve as a crucial checkpoint for substrate discrimination.