Is there an engine thrust level limit for deploying thrust reversers? Does an engine have to be at idle thrust for the reversers to deploy? If the engine is at higher than idle thrust, will it slow down to deploy the reversers and then speed up again, or can it just deploy the reversers at the higher thrust?

I am also asking about turboprops going into beta range.

I had this question based on the discussion on this question:

What to do when you accidentally land on a runway thats borderline long enough to land on?
Engines must be at idle thrust to enter reverse thrust.  This may not be 100% true of the physical action of engine entering reverse thrust (opening the buckets or translating the cowling), but it is required by the thrust levers.  In all airplanes I'm familiar with the thrust levers must be at idle to enter the reverse regime,  In the EMB-145 the reversage was below idle (i.e. you keep moving the levers aft) through a gate.  Even if the engine is capable of entering reverse thrust not at idle, there is no way to command it without first being at idle.