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A knot K in the 3-sphere is handle-ribbon in a homotopy 4-ball B if K bounds a properly embedded disk in B whose exterior has a handle decomposition made up of a 0-handle, 1-handles, and 2-handles. As such, handle-ribbon knots serve as an intermediary between slice knots and ribbon knots: Every ribbon knot is handle-ribbon, and every handle-ribbon knot is slice. We present two alternative characterizations of handle-ribbon knots, one using derivative links on a Seifert surface and the other using Morse-2 functions, where the latter approach also gives rise to an interesting family of trisections. This is joint work with Maggie Miller.