1. In a computing system having a plurality of processes running therein, each process having a memory space that is backed by machine memory of the computer system and a corresponding thinly-provisioned swap file, a method for swapping out contents of a page of memory from the machine memory to a thinly-provisioned swap file, said method comprising: determining that the thinly-provisioned swap file needs additional capacity to store the contents of the page; moving a storage block from a thickly-provisioned swap reservation file to the swap file; and storing the contents of the page to the moved storage block.