  We first review the $L^2$ bilinear generalizations of the $L^4$ estimate of
Strichartz for solutions of the homogeneous 3D wave equation, and give a short
proof based solely on an estimate for the volume of intersection of two
thickened spheres. We then go on to prove a number of new results, the main
theme being how additional, anisotropic Fourier restrictions influence the
estimates. Moreover, we prove some refinements which are able to simultaneously
detect both concentrations and nonconcentrations in Fourier space.
