1. A computer program product for managing data sets in a storage, the computer program product comprising a computer readable storage medium having computer readable program code embodied therein that executes to perform operations, the operations comprising: receiving a request for additional storage space to allocate to a data set stored in a first managed space in the storage; determining a revised amount of storage space for the data set comprising at least an amount of space currently allocated to the data set in the first managed space and the additional storage space; determining whether the revised amount of storage space exceeds a value; allocating, in response to determining that the revised amount of storage space exceeds the value, the revised amount of storage space in allocated storage space in a second managed space of the storage; extending the data set including the additional storage space into the first managed space in response to determining that the revised amount of storage space does not exceed the value; and storing the data set in the allocated storage space in the second managed space.