Two models are proposed for the probability density function (p.d.f.) of the amplitude fluctuations that arise when short-duration sound pulses are transmitted under shallow-water conditions. The models are derived for the conditions in which the prevailing surface-wind directions are parallel and perpendicular to the line of transmission. The probability density functions obtained from the models are compared with experimentally measured p.d.f.s and are found to be in excellent agreement. The models are then used to predict the bit-error probability in a binary underwater amplitude-shift-keyed (a.s.k) data-transmission system and the results are compared with experimentally measured error probabilities. It is found that the measured error probabilities lie between the values computed using the p.d.f. models and it is conjectured that the proposed models provide approximate upper and lower bounds to the average error probability in a.s.k. underwater data-transmission systems. Finally, the p.d.f. models are used to compute new receiver-operating-characteristic (r.o.c.) curves.