  Let $R$ be a Cohen-Macaulay local ring possessing a canonical module. We
compare the initial and terminal Betti numbers of modules in a series of
nontrivial cases. We pay special attention to the Betti numbers of the
canonical module. Also, we compute $\beta_0(\omega_{\frac{R}{I}})$ in some
cases, where $I$ is a product of two ideals.
