A computer-implemented method for facilitating processing within a computing environment, the computer-implemented method comprising: determining whether an access intent control field (603, 604) of an instruction includes a hold value or a release value, the hold value being a hold designation for a storage operand request of a subsequent instruction to a storage location shared by multiple processing units of a computing environment, and the release value being a release designation for the storage location shared by multiple processing units of the computing environment; and controlling, at least in part, processing of the subsequent instruction dependent on whether the access intent control field of the instruction includes the hold value, the controlling comprising: ascertaining whether a state of a corresponding cache line in private cache (204, 306a, 306n) used for processing the storage operand request is owned exclusively by the processing unit; and based on determining that the storage operand request is designated hold, and that the state of the corresponding cache line in private cache used for processing the storage operand request is owned exclusively, continuing to hold the corresponding cache line in private cache exclusively after completing processing of the storage operand request, the continuing to hold including initiating a counter to facilitate the continuing hold for a desired interval. determining whether an access intent control field (603, 604) of an instruction includes a hold value or a release value, the hold value being a hold designation for a storage operand request of a subsequent instruction to a storage location shared by multiple processing units of a computing environment, and the release value being a release designation for the storage location shared by multiple processing units of the computing environment; and controlling, at least in part, processing of the subsequent instruction dependent on whether the access intent control field of the instruction includes the hold value, the controlling comprising: ascertaining whether a state of a corresponding cache line in private cache (204, 306a, 306n) used for processing the storage operand request is owned exclusively by the processing unit; and based on determining that the storage operand request is designated hold, and that the state of the corresponding cache line in private cache used for processing the storage operand request is owned exclusively, continuing to hold the corresponding cache line in private cache exclusively after completing processing of the storage operand request, the continuing to hold including initiating a counter to facilitate the continuing hold for a desired interval. ascertaining whether a state of a corresponding cache line in private cache (204, 306a, 306n) used for processing the storage operand request is owned exclusively by the processing unit; and based on determining that the storage operand request is designated hold, and that the state of the corresponding cache line in private cache used for processing the storage operand request is owned exclusively, continuing to hold the corresponding cache line in private cache exclusively after completing processing of the storage operand request, the continuing to hold including initiating a counter to facilitate the continuing hold for a desired interval.