This study analyzes cloud top brightness temperature (CTBT) and cloud-to-ground (CG) lightning stroke densities over the continental United States from May to October 1999. The good coverage of the study period and the large number of colocated stroke densities and CTBTs provide robust statistics. Prior studies have reported nonlinear lightning flash rate increase with cloud depth. In this work, some support is found for such relationships, in the particular case of CG strokes. The likelihood of CG stroke occurrence and of high CG stroke density is higher if CTBTs are among the coldest. However, a monthly and regional analysis of CTBT/stroke density correspondences reveals quasi-constant overall stroke densities for CTBTs warmer than about -55¿C (most of the CTBT/stroke density samples). Overall stroke densities increase as CTBT decreases only for CTBTs colder than about -55¿C. This is consistent with a statistical but not instantaneous lightning flash rate/cloud depth relationship. Thus the number of ¿CG strokes per CG-producing cloud top surface area per hour, integrated over monthly periods in each geographical region, is approximately constant versus time depending only on the region.