A computer system (10) implements a memory allocator that employs a data structure (FIG. 3) to maintain an inventory of dynamically allocated memory available to receive new data. It receives from one or more programs requests that it allocate memory from a dynamically allocable memory “heap.” It responds to such requests by performing the requested allocation and removing the thus-allocated memory block from the inventory. Conversely, it adds to the inventory memory blocks that the supported program or programs request be freed. In the process, it monitors the frequencies with which memory blocks of various sizes are allocated, and it projects from those frequencies future-demand values for memory blocks of those sizes. It then splits larger blocks into smaller ones preemptively, i.e., before a request for the result of the splitting. To split a relatively large block preemptively in order to meet an expected request for a smaller block, it bases its selection of the larger block to be split on whether the supply of free blocks of that size is great enough to meet the expected demand for such blocks. It also splits blocks reactively, i.e., in response to a previously made request for a block that will result from the splitting operation.