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 \rightarrow - 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 .