1. A method of facilitating processing in a computing environment having a plurality of processors, the method comprising: executing by a processor of the computing environment a machine instruction, the machine instruction specifying a nonquiescing control (NQ) to control whether a quiescing, operation is to be performed, a storage key, and one or more values to be used to set the storage key, the storage key being associated with a block of storage, and wherein the executing comprises: based on the NQ being a first value indicating that a quiescing operation is to be performed, performing a)-c) comprising: a) initiating quiesce of other processors of the computing environment capable of accessing said storage key during execution of the machine instruction; b) based on the other processors reaching a quiesce point, storing at least one value of the one or more values in the storage key associated with the block of main storage; and c) initiating an end to the quiesce; and based on the NQ being a second value indicating that a quiescing operation is not to be performed, storing at least one value of the one or more values in the storage key associated with the block of main storage absent quiescing other processors of the computing environment capable of accessing said storage key, the at least one value changing at least one of an access control component and a fetch protection component of the storage key.