  We examine the evolution of quintessence models with potentials satisfying
(V'/V)^2<<1 and V"/V<<1, in the case where the initial field velocity is
nonzero. We derive an analytic approximation for the evolution of the equation
of state parameter, w, for the quintessence field. We show that such models are
characterized by an initial rapid freezing phase, in which the equation of
state parameter w decreases with time, followed by slow thawing evolution, for
which w increases with time. These models resemble constant-V models at early
times but diverge at late times. Our analytic approximation gives results in
excellent agreement with exact numerical evolution.
