A modified regularized least squares pKa spectrum approach is proposed to determine proton stability constants and concentrations for binding sites on hydrous ferric oxide (HFO) and aluminum oxide surfaces. Acid-base titration data are fit to a continuous binding site model for the system represented as a pKa spectrum. The modified parameter fitting method optimizes simultaneously for both smoothness of the pKa spectrum and goodness-of-fit, whereas other methods optimize for goodness-of-fit given a fixed smoothness factor. The modified method is tested with aluminum oxide and recovers values consistent with theoretical values. The regularized pKa spectrum method optimized for smoothness is applied to prepared samples of two types of HFO. The prepared HFO samples differ only in the total iron concentration of the parent solution. The resultant pKa distributions are compared to proton binding constants from MUSIC model results for crystalline iron oxides. The types of binding sites in the HFO sample are consistent with theoretical binding site stability constants for crystalline iron oxides. Overall, the prepared HFO samples have binding constants most consistent with values for lepidocrocite and goethite.