The described embodiments include a computing device with two or more translation lookaside buffers (TLB) that performs operations for handling entries in the TLBs. During operation, the computing device maintains lease values for entries in the TLBs, the lease values representing times until leases for the entries expire, wherein a given entry in the TLB is invalid when the associated lease has expired. The computing device uses the lease value to control operations that are allowed to be performed using information from the entries in the TLBs. In addition, the computing device maintains, in a page table, longest lease values for page table entries indicating when corresponding longest leases for entries in TLBs expire. The longest lease values are used to determine when and if a TLB shootdown is to be performed.