We present a detailed account of photoluminescence measurements, including thermal activation energy and transient luminescence decay time results, on isoelectronic bound excitons associated with complex binding centers containing either of the deep acceptors In or Tl. The number of these centers can be greatly increased by a simple thermal quenching procedure, resulting in very intense photoluminescence due to the high radiative efficiencies of these new centers. The In and Tl spectra show both striking similarities and differences, which lead to some tentative conclusions as to the nature of the binding centers. In particular, the Tl-related center displays a number of unique features which lead us to suggest that it can exist in two forms, having quite different luminescence properties. These two forms exist in thermal equilibrium with each other, and we propose that they differ in that the low temperature center binds a lattice defect, either a Si interstitial or a vacancy, whereas the high temperature center results from the thermal 'evaporation' of this defect.