A technique for efficiently boosting the priority of a preemptable data reader while resolving races between the priority boosting and the reader exiting a critical section or terminating in order to eliminate impediments to grace period processing that defers the destruction of one or more shared data elements that may be referenced by the reader until the reader is no longer capable of referencing the one or more data elements. A determination is made that the reader is in a read-side critical section and the reader is designated as a candidate for priority boosting. A verification is made that the reader has not exited its critical section or terminated, and the reader's priority is boosted to expedite its completion of the critical section. The reader's priority is decreased following its completion of the critical section.