[en] A long-established technique for accumulating high current in a storage ring is to inject additional beam off-momentum and move it into the main beam stack by rf acceleration. This procedure necessarily dilutes the longitudinal phase space density, because the rf perturbs the stack as the new beam approaches closely in momentum. For accumulators that use beam cooling to obtain a high phase space density, this perturbation may result in an unacceptable performance limitation. Using broadband rf to establish and manipulate azimuthal barriers to the motion of the stack and injected beam permits practically dilution-free longitudinal phase space stacking. The concept is described and illustrated with a detailed example which pertains to the Fermilab Recycler ring