We recently presented a model of a compactly generated and topological
ly trivial time-machine spacetime which satisfies the weak energy cond
ition all the way up to the critical time slice (achronal hypersurface
) in which a closed causal curve appears. Here we modify the above mod
el so as to satisfy not only the weak energy condition, but also the d
ominant energy condition, up to that critical time slice.