We have studied exciton unbinding in empty and p-doped quantum wells, using magnetophotoluminescence excitation measurements. The use of p-type quantum wells allows us to discriminate unambiguously between exciton bleaching by Coulomb screening and by the Pauli exclusion principle. We found that the ground-state heavy-hole exciton, which experiences both effects, is unbound at hole densities in the range (6-9) x 10(15) m(-2). In contrast, the ground-state light-hole and first excited heavy-hole excitons, which are only screened by the Coulomb interaction, still have a finite binding energy at these densities. However, for both bands, its Value is far below what is found in an undoped well. Furthermore, we found a strong indication that, in p-doped wells, the excitons of excited subbands are less efficiently screened than those of the Light-hole ground state, due to the lesser overlap of the screening ground-state heavy holes with the excited subbands than with the ground-state light holes.