I know a place (around RESMI, for those who know it), where an explosive decomp at FL370 and the subsequent emergency descent to FL100 would let the traffic cross 26 levels, a dozen flows, 4 sectors, 2 ACCs and CDG approach in 2 minutes.
In this case, the biggest problem for us is to co-ordinate with lower sectors.
When one starts the descent, we get the information 4 seconds later. If we're not dealing with something else, we'll see it straight away. Expect then ONE message (that you won't hear) to confirm your clearance.
4 more seconds later, when we see that you've lost 1000', the emergency descent becomes obvious and we begin the co-ordinations with lower sectors.
Sqwak 7700
We've got automated systems to show a traffic performing an emergency descent to sectors who wouldn't see it in normal situation (filters to avoid overflow of useless informations), sqwaking 7700 as soon as possible forces the system and the traffic will immediately show in orange on every sector at once, which can make us save precious seconds.
Turn
In normal situations, when we vector a traffic, we anticipate the new trajectory. As we don't know your intentions, when you turn, we've got the information about the new trajectory only 10-15 seconds (5000' ?) after the end of the turn (because of the caculations, averages, smoothenings included in the radar system). If you turn too often, "cleaning" your way in lower levels becomes much more difficult.