  In this paper, we initiate our investigation of log canonical models for the
moduli space of curves with the boundary divisor $\a \d$ as we decrease $\a$
from 1 to 0. We prove that for the first critical value $\a = 9/11$, the log
canonical model is isomorphic to the moduli space of pseudostable curves, which
have nodes and cusps as singularities. We also show that $\a = 7/10$ is the
next critical value, i.e., the log canonical model stays the same in the
interval $(7/10, 9/11]$. In the appendix, we develop a theory of log canonical
models of stacks that explains how these can be expressed in terms of the
coarse moduli space.
