We have studied exciton unbinding in empty and p-doped single and double quantum wells, using magneto-photoluminescence excitation measurements. The use of p-type heterostructures allows to discriminate unambiguously between exciton bleaching by Coulomb screening and by the Pauli exclusion principle. The groundstate heavy-hole exciton, which experiences both effects, is unbound at hole densities in the range (6 to 11) x 10(15) m(-2). In contrast, the groundstate light-hole and first excited heavy-hole excitons: which only experience Coulomb screening, still have a finite binding energy at these densities. We found that the excitons of excited subbands are far less efficiently screened than those of the light-hole groundstate, due to the lesser overlap of the screening groundstate heavy holes with the excited subbands than with the groundstate light holes.