In certain Hiroshima neighborhoods, radiation measurements using thermoluminescence dosimetry (TLD) exceed what can be explained by the initial gamma-ray doses and uncertainties from the Dosimetry System 2002 (DS02). This problem was not previously recognized as being isolated to certain parts of that city. The ratio between TLD measurements and DS02 dose calculations for gamma rays appear to grow larger than unity up to more than three with increasing ground range, but closer examination shows the excess TLD dose (0.1, 0.2, or possibly up to 0.8 Gray) is correlated with certain neighborhoods and could be due to radioactive fallout. At Nagasaki, the TLD measurements do not show this same excess, probably because there were no TLD measurements taken more than 800 m downwind (eastward) from the Nagasaki hypocenter, so that any small excess TLD dose was masked by larger initial gamma-ray doses of 25-80 Gray in the few downwind samples. The DS02 Report had noted many measurements lower than the DS02 calculation for several Nagasaki TLD samples, independent of ground range. This was explained as being the result of previously unaccounted urban shielding which was observed from Nagasaki pre-bomb aerial photos. However, the Hiroshima excess TLD dose issue was not resolved. If the excess TLD doses at Hiroshima are an indication of fallout, it may be possible to use additional TLD studies to make better estimates of the locations and radiation doses to survivors from the fallout after the bombings at both cities.