A couple more points - Pete backs up his advice with examples (mostly H500's if memory serves me right) where, following an engine failure the pilot(s) elected to dive towards the ground (pushing forward on cyclic) at the expense of rotor RPM. All of the examples showed very heavy landings on the left side of the machine due to lack of control due to low rotor RPM.
Having done quite a few HV demos in OH-58/Bell 206 to budding experimental test pilots, I can attest that in the high hover case, it's necessary to maintain a level attitude following the failure - mostly with a small amount of aft cyclic.
I remember hearing that during the HV tests for one of the Bell teetering rotor helicopters that the test pilot pushed forward on the cyclic when the (very) high hover point was first tested - his comment after several minutes of silence following the nearly vertical nose-down attitude that was observed was something to the effect of 'Don't push forward'.
On the other hand, don't be slavish - one US military helicopter training school used to insist on aft cyclic in a low altitude hovering engine failure when it wasn't needed.
Something else to remember is that real engine failures are not like the training ones- every single pilot I've talked to who has had a real engine failure in a single engine helo has commented on the very large surprise factor compared to training autorotations.