  The wave-Sobolev spaces $H^{s,b}$ are $L^2$-based Sobolev spaces on the
Minkowski space-time $\R^{1+n}$, with Fourier weights are adapted to the symbol
of the d'Alembertian. They are a standard tool in the study of regularity
properties of nonlinear wave equations, and in such applications the need
arises for product estimates in these spaces. Unfortunately, it seems that with
every new application some estimates come up which have not yet appeared in the
literature, and then one has to resort to a set of well-established procedures
for proving the missing estimates. To relieve the tedium of having to
constantly fill in such gaps "by hand", we make here a systematic effort to
determine the complete set of estimates in the bilinear case. We determine a
set of necessary conditions for a product estimate $H^{s_1,b_1} \cdot
H^{s_2,b_2} \hookrightarrow H^{-s_0,-b_0}$ to hold. These conditions define a
polyhedron $\Omega$ in the space $\R^6$ of exponents
$(s_0,s_1,s_2,b_0,b_1,b_2)$. We then show, in space dimension $n=3$, that all
points in the interior of $\Omega$, and all points on the faces minus the
edges, give product estimates. We can also allow some but not all points on the
edges, but here we do not claim to have the sharp result. The corresponding
result for $n=2$ and $n=1$ will be published elsewhere.
