This paper presents early results of a trial of a three-fractions-per-day (TID) regimen that is more convenient to schedule than the Continuous Hyperfractionated Accelerated Radiotherapy (CHART) protocol currently being tested in Europe. The treatment schedule used in the CHART regimen has been modified from 36 fractions of 1.5 Gy TID in 12 days to 72 fractions of 1.1 Gy in 24 treatment days, with all fractions delivered during normal working hours. With no weekend treatments, the entire course of radiotherapy is completed in less than 5 weeks. The doses used were determined using the L-Q model, with correction for incomplete repair between fractions and for accelerated repopulation of cancer cells. Comparison with historical controls shows statistically significant improvements both in CR rates for the primary tumor and in acute toxicity, as measured by reduced treatment interruptions. L-Q model calculations predict that, compared to the highest dose achieved in previous studies without exceeding tolerance, we are able to obtain a 12% increase in bioeffect dose to the primary tumor due to accelerating the treatment. An analysis of the potential tumoricidal effectiveness of this new treatment regimen shows that it should be better than several other accelerated fractionation schedules being tested for all values of Tpot. For short Tpot times, the advantage may be as much as one log cell kill, corresponding to a 10-15% potential improvement in local control.