Numerical and experimental results on the effect of randomness in GaAs/Al0.3Ga0.7As superlattices having a small number of randomly distributed well widths are reported. The numerical results indicate the splitting of the extended state miniband into sub-minibands of localized states having a disorder-induced fine structure. The comparison between the experimental results for low-temperature absorption spectra and the computed joint density of states of the investigated samples confirms the predicted features. The high-temperature photoluminescence intensity of random superlattices is observed to be enhanced with respect to the ordered case.