We conducted a systematic study of the disorder dependence of the termination of superconductivity, at high magnetic fields (B), of amorphous indium oxide films. Our lower disorder films show conventional behavior where superconductivity is terminated with a transition to a metallic state at a well-defined critical field, B-c2. Our higher-disorder samples undergo a B-induced transition into a strongly insulating state, which terminates at higher B's forming an insulating peak. We demonstrate that the B terminating this peak coincides with B-c2 of the lower disorder samples. Additionally, we show that, beyond this field, these samples enter a different insulating state in which the magnetic field dependence of the resistance is weak. These results provide crucial evidence for the importance of Cooper-pairing in the insulating peak regime.