Rad23 is an adaptor protein that binds to both ubiquitinated substrates and to the proteasome. Despite its association with the proteasome, Rad23 escapes degradation. Here we show that Rad23 remains stable because it lacks an effective initiation region at which the proteasome can engage the protein and unfold it. Rad23 contains several internal, unstructured loops, but these are too short to act as initiation regions. Experiments with model proteins show that internal loops must be surprisingly long to engage the proteasome and support degradation. These length requirements are not specific to Rad23 and reflect a general property of the proteasome.