Q-compensation of seismic primaries that have reflected from a stratified, absorptive-dispersive medium may be posed as a direct, nonlinear inverse scattering problem. If the reference medium is chosen to be nonattenuating and homogeneous, an inverse-scattering Q-compensation procedure may be derived that is highly nonlinear in the data, but which operates in the absence of prior knowledge of the properties of the subsurface, including its Q structure. It is arrived at by (1) performing an order-by-order inversion of a subset of the Born series, (2) isolating and extracting a component of the resulting nonlinear inversion equations argued to enact Q- compensation, and (3) mapping the result back to data space. Once derived, the procedure can be understood in terms of nonlinear interaction of the input primary reflection data: the attenuation of deeper primaries is corrected by an operator built (automatically) using the angle- and frequency variations of all shallower primaries. A simple synthetic example demonstrates the viability of the procedure in the presence of densely sampled, broadband reflection data.