  We examine models in which the dark energy density increases with time (so
that the equation-of-state parameter w satisfies w < -1), but w approaches -1
asymptotically, such that there is no future singularity. We refine previous
calculations to determine the conditions necessary to produce this evolution.
Such models can display arbitrarily rapid expansion in the near future, leading
to the destruction of all bound structures (a "little rip"). We determine
observational constraints on these models and calculate the point at which the
disintegration of bound structures occurs. For the same present-day value of w,
a big rip with constant w disintegrates bound structures earlier than a little
rip.
