  We propose a time stepping scheme for the space-time systems obtained from
Galerkin time-domain boundary element methods for the wave equation. Based on
extrapolation, the method proves stable, becomes exact for increasing degrees
of freedom and can be used either as a preconditioner, or as an efficient
standalone solver for scattering problems with smooth solutions. It also
significantly reduces the number of GMRES iterations for screen problems, with
less regularity, and we explore its limitations for enriched methods based on
non-polynomial approximation spaces.
