  In previous work we showed that for a manifold $M$, whose universal cover has
infinitely many boundary components, the set of essential ideal triangulations
of $M$ is connected via 2-3, 3-2, 0-2, and 2-0 moves. Here we show that this
set is also connected via 2-3 and 3-2 moves alone, if we ignore those
triangulations for which no 2-3 move results in an essential triangulation. If
we also allow V-moves and their inverses then the full set of essential ideal
triangulations of $M$ is once again connected. These results also hold if we
replace essential triangulations with $L$-essential triangulations.
