The possibility of binding excitons to complex-type defects in GaAs is discussed, with reference to recent photoluminescence data on Cu-related centers. The apparent absence of bound excitons (BEs) associated with certain complex-type acceptors may be explained as a consequence of a local compressional strain field at the defect. Such a field will decrease the binding energy of electron states derived from the 1 conduction-band minimum in GaAs, so that they ultimately become resonant with the band in the limit of a strong field. A similar effect on the BE electron state is expected for neutral-complex defects, particularly if they involve two interstitial species. Only one example of an exciton binding to a neutral complex was found in GaAs so far. It involves a tensional local strain field, in which case the BE electron localization becomes stabilized.