I present observations of the Pa-alpha emission line in the extremely luminous, IRAS-selected galaxies IRAS 20460 + 1925 and IRAS 23060 + 0505. These objects have previously been classified as Seyfert 2 galaxies based on their optical emission-line spectra, but their luminosities (greater than 10(12) L.) are characteristic of QSOs. The widths of H-alpha are 2500 and 550 km s-1 (FWHM) for IRAS 20460 + 1925 and IRAS 23060 + 0505, respectively. The Pa-alpha observations reveal the presence of broad lines of width 2940 (+/- 160) and 2900 (+/- 270) km s-1 (FWHM, both corrected for the instrumental broadening). Using the narrow line strengths derived from the reddened optical line spectra, the narrow Pa-alpha line contributions to the observed Pa-alpha emission profiles have been removed. The resulting broad-line widths are approximately 3860 and approximately 4780 km s-1 for IRAS 20460 + 1925 and IRAS 23060 + 0505, respectively. The Pa-alpha measurements place constraints on the visual extinction to the BLR, A-upsilon > 3.6 for IRAS 20460 + 1925 and A-upsilon greater-than-or-similar-to 4.4 for IRAS 23060 + 0505. Considering their bolometric luminosities and the presence of broad emission lines, I suggest that IRAS 20460 + 1925 and IRAS 23060 + 0505 should be reclassified as QSOs.