The rate of self-propulsion of a doubly-infinite flexible sheet due to transverse waving oscillations in a viscous fluid is shown to decrease with increasing frequency, at a fixed (small) wave amplitude. This result differs from that of Reynolds (1965) who included local inertia, and thereby predicted that the swimming speed increases above the limiting value given by Taylor (1951) at zero frequency. The error in Reynolds’ work is due to his neglect of the simultaneous effect of convection, which induces a non-uniform mean second-order flow, with direction such as to oppose propulsion. Some other results concerning swimming sheets are presented.