An integrated circuit includes multiple power domains. Supply current switch circuits (SCSCs) are distributed across each power domain. When a signal is present on a control node within a SCSC, the SCSC couples a local supply bus of the power domain to a global supply bus. An enable signal path extends through the SCSCs so that an enable signal can be propagated down a chain of SCSCs from control node to control node, thereby turning the SCSCs on one by one. When the domain is to be powered up, a control circuit asserts an enable signal that propagates down a first chain of SCSCs. After a programmable amount of time, the control circuit asserts a second enable signal that propagates down a second chain. By spreading the turning on of SCSCs over time, large currents that would otherwise be associated with coupling the local and global buses together are avoided.