We investigated how Escherichia coli ClpXP targets the helicase-nuclease (HsdR) subunit of the bacterial Type I restriction-modification enzyme EcoKI during restriction alleviation (RA). RA is a temporary reduction in endonuclease activity that occurs when Type I enzymes bind unmodified recognition sites on the host genome. These conditions arise upon acquisition of a new system by a naïve host, upon generation of new sites by genome rearrangement/mutation or during homologous recombination between hemimethylated DNA. Using recombinant DNA and proteins in vitro, we demonstrate that ClpXP targets EcoKI HsdR during dsDNA translocation on circular DNA but not on linear DNA. Protein roadblocks did not activate HsdR proteolysis. We suggest that DNA translocation lifetime, which is elevated on circular DNA relative to linear DNA, is important to RA. To identify the ClpX degradation tag (degron) in HsdR, we used bioinformatics and biochemical assays to design N- and C-terminal mutations that were analysed in vitro and in vivo. None of the mutants produced a phenotype consistent with loss of the degron, suggesting an as-yet-unidentified recognition pathway. We note that an EcoKI nuclease mutant still produces cell death in a clpx(-) strain, consistent with DNA damage induced by unregulated motor activity.