  We examine dark energy models in which a phantom field $\phi$ is rolling near
a local minimum of its potential $V(\phi)$.We require that $(1/V)(dV/d\phi) \ll
1$, but $(1/V)(d^2 V/d\phi^2)$ can be large. Using techniques developed in the
context of hilltop quintessence, we derive a general expression for $w$ as a
function of the scale factor, and as in the hilltop case, we find that the
dynamics of the field depend on the value of $(1/V)(d^2 V/d\phi^2)$ near the
mimimum. Our general result gives a value for $w$ that is within 1% of the true
(numerically-derived) value for all of the particular cases examined. Our
expression for $w(a)$ reduces to the previously-derived phantom slow-roll
result of Sen and Scherrer in the limit where the potential is flat,
$(1/V)(dV/d\phi) \ll 1$.
