The present writer has discussed various aspects of propagation in sediment channels [J. Acoust.Soc. Am.70, 820–824 (1981)]. A simplifying assumption was thatcw, the speed of sound in the water, is constant everywhere. In this sequel it is more realistically assumed thatcwdecreases slowly and linearly with height above the water–sediment interface. Consequently an acoustic barrier exists from the interface to, typically, 100–200 m above it. Acoustic energy in a signal traveling along the sediment channel can tunnel upward through the barrier, thereby causing a ‘‘leakage’’ attenuation along the channel. Equations are derived to describe the acoustic field both in and above the barrier, and a long‐known method yields the amplitude attenuation factor caused by leakage. Using numerical examples from the 1981 article, we find that the leakage factor is a negligible 1% of the factor caused by absorption in the sediment. In this case, the approximation of constantcwwas justified, but for a normal mode nearer cutoff the leakage would increase considerably.