Low-frequency propagation in a uniform liquid layer over a “slow” viscoelastic bottom of infinite depth is analyzed. True absorption in the liquid layer is ignored, but the Lamé constants of the solid are allowed to be complex; that is, the corresponding compressional and transverse waves may suffer absorption. The compressional wave speed c2 in the bottom is assumed to exceed the speed c1 in the liquid, which in turn exceeds the transverse wave speed ct in the bottom. The eigenvalue equation for normal modes in the liquid layer is derived. Regardless of absorptions in the bottom, this equation yields complex values for the phase velocities of normal modes in the liquid, so that attenuation exists. Generally the real parts of these velocities are altered, relative to the Pekeris problem of liquid over liquid, as if the density of the lower material were decreased. Three special examples are displayed: (a) Attenuation over a nonabsorbing solid bottom; (b) attenuation over an absorbing bottom of Hycar rubber, used in an earlier model test of shallow-water propagation; (c) the joint effects of a transverse wave and small absorptions in the bottom for a mode far from cutoff, to show the degree of interdependence among the attenuations.