We generate a natural hierarchy of equivalences for asynchronous name-passing process calculi from simple variations on Milner and Sangiorgi’s definition of weak barbed bisimulation. The π-calculus, used here, and the join calculus are examples of such calculi. We prove that barbed congruence coincides with Honda and Yoshida’s reduction equivalence, and with asynchronous labeled bisimulation when the calculus includes name matching, thus closing those two conjectures. We also show that barbed congruence is coarser when only one barb is tested. For the π-calculus, it becomes a limit bisimulation, whereas for the join calculus, it coincides with both fair testing equivalence and with the weak barbed version of Sjodin and Parrow’s ¨ coupled simulation.