We examine phantom dark energy models derived from a scalar field with a negative kinetic term for which V ( \phi ) \rightarrow \infty asymptotically .
All such models can be divided into three classes , corresponding to an equation of state parameter w _ { \phi } with asymptotic behavior w _ { \phi } \rightarrow - 1 , w _ { \phi } \rightarrow w _ { 0 } < -1 , and w _ { \phi } \rightarrow - \infty .
We derive the conditions on the potential V ( \phi ) which lead to each of these three types of behavior .
For models with w _ { \phi } \rightarrow - 1 , we derive the conditions on V ( \phi ) which determine whether or not such models produce a future big rip .
Observational constraints are derived on two classes of these models : power-law potentials with V ( \phi ) = \lambda \phi ^ { \alpha } ( with \alpha positive or negative ) and exponential potentials of the form V ( \phi ) = \beta e ^ { \lambda \phi ^ { \alpha } } .
It is shown that these models spend more time in a state with \Omega _ { m } \sim \Omega _ { \phi } than do corresponding models with a constant value of w _ { \phi } , thus providing a more satisfactory solution to the coincidence problem .