A computer system provides for rapid power-on operations on virtual machines (VMs) with a virtual memory space including a reservation from machine memory and a small or no swap size. When the computer system powers on a VM, the computer system creates a physical memory space for the VM with a size larger than the minimum memory reservation for the VM and a swap space with a size less than the difference between the size of the virtual memory space and the minimum memory reservation. Subsequently, the computer system iteratively decreases the size of the physical memory space for the VM and increases the size of the swap space for the VM until the size of the physical memory space equals the minimum size of the memory reservation, which may be the amount of the virtual space that is guaranteed to be backed by machine memory.