It is generally assumed that protein clients fold following their release from chaperones instead of folding while remaining chaperone-bound, in part because binding is assumed to constrain the mobility of bound clients. Previously, we made the surprising observation that the ATP-independent chaperone Spy allows its client protein Im7 to fold into the native state while continuously bound to the chaperone. Spy apparently permits sufficient client mobility to allow folding to occur while chaperone bound. Here, we show that strengthening the interaction between Spy and a recently discovered client SH3 strongly inhibits the ability of the client to fold while chaperone bound. The more tightly Spy binds to its client, the more it slows the folding rate of the bound client. Efficient chaperone-mediated folding while bound appears to represent an evolutionary balance between interactions of sufficient strength to mediate folding and interactions that are too tight, which tend to inhibit folding.