Temporarily suppressing processing of a restrained storage operand request

Processing of a storage operand request identified as restrained is selectively, temporarily suppressed. The processing includes determining whether a storage operand request to a common storage location shared by multiple processing units of a computing environment is restrained, and based on determining that the storage operand request is restrained, then temporarily suppressing requesting access to the common storage location pursuant to the storage operand request. The processing unit performing the processing may proceed with processing of the restrained storage operand request, without performing the suppressing, where the processing can be accomplished using cache private to the processing unit. Otherwise the suppressing may continue until an instruction, or operation of an instruction, associated with the storage operand request is next to complete.