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We show that the spectral shape of the low energy tails found for the time-integrated spectra of gamma-ray bursts, even in the absence of strong synchrotron cooling, can be significantly softer than the ν F_ν∝ν^4/3 asymptote predicted by synchrotron shock models. As we have noted in a previous work, blast wave deceleration via interaction with ambient material causes the characteristic electron injection energy to decrease in proportion to the bulk Lorentz factor of the blast wave, and underdoi:10.1086/306991 fatcat:itvgvfusyfgzthcuqoi6otqnl4