A method for predictively allocating space in a database system includes detecting an access request for a data set, evaluating a growth rate of the data set to determine a predicted increase in size of the data set, and in response dynamically altering an attribute of an allocation for the data set. Attributes altered include the size of volumes and the number of volumes comprising the data set. The method may include setting a flag indicating an instruction to rewrite the data set if the evaluation indicates that rewriting is needed to accommodate the predicted increase in size. The method may include rewriting the data set from a lower address space of a volume to a higher address space of the volume if the size of the data set is equal to or greater than an allocation increment of the upper address space. A corresponding apparatus and computer program product are also disclosed herein.