Replacing a failing physical processor in a computer supporting multiple logical partitions, where the logical partitions include dedicated partitions and shared processor partitions, the dedicated partitions are supported by virtual processors having assigned physical processors, and the shared processor partitions are supported by pools of virtual processors. The pools of virtual processors have assigned physical processors. Embodiments operate generally by assigning priorities to the dedicated partitions and to the pools of virtual processors; detecting a checkstop of a failing physical processor; retrieving the failing physical processor's state; replacing by a hypervisor the failing physical processor with a replacement physical processor assigned to a dedicated partition or pool, which dedicated partition or pool has the lowest priority among the priorities of the dedicated partitions and pools; and assigning the retrieved state of the failing physical processor as the state of the replacement physical processor.