A computer system provides a mechanism for assuring a safe, non-preemptible access to a private data area (PRDA) belonging to a CPU. PRDA accesses generally include obtaining an address of a PRDA and performing operations on the PRDA using the obtained address. Safe, non-preemptible access to a PRDA generally ensures that a context accesses the PRDA of the CPU on which the context is executing, but not the PRDA of another CPU. While a context executes on a first CPU, the context obtains the address of the PRDA. After the context is migrated to a second CPU, the context performs one or more operations on the PRDA belonging to the second CPU using the address obtained while the context executed on the first CPU. In another embodiment, preemption and possible migration of a context from one CPU to another CPU is delayed while a context executes non-preemptible code.