We have performed an optimization study of the mid-infrared photoresponse of p-type GaAs/AlGaAs Quantum Well Infrared Photodetectors (QWIPs) designed for normal incidence detection. In these p-type quantum wells, normal incidence absorption is allowed (by the dipole selection rules for optical transitions) especially for transitions from the heavy-hole ground state to the second light-hole state. Previous theoretical modeling predicted that this transition will produce the strongest bound-to-continuum infrared absorption when the second light-hole state is located very near the top of the GaAs quantum well. For AlGaAs barrier layers with 30% aluminum, our modeling showed that a well width between 45Å and 50Å would optimize the normal incidence photoresponse of this p-type QWIP. In this work, photore^oonse spectra are reported for well widths ranging from 40Å to 65Å. A series of samples were tudied in which only the GaAs well width was varied in two monolayer increments, from 11 to 20 monolayers. Photoluminescence and X-ray diffraction measurements were used to verify the composition, well width, and structural quality of each sample. This study verified that the spectral range of the normal incidence photoresponse is narrower, as predicted by theory, for well widths in which the second light-hole state approaches the top of the valence band well.