A broad range of heavy-ion-induced fusion excitation functions are classically analyzed. The fusion-barrier parameters are compared with predictions of the proximity potential, a Yukawa-plus-exponential model, and a modified Woods-Saxon potential. The Yukawa-plus-exponential model is found to give the best overall agreement with the data. The proximity potential is too shallow, but would be in closer agreement with data if a necking contribution were added. NUCLEAR REACTIONS Extracted fusion barriers and radii from fusion data with heavy ions, compared several theoretical models.