appropriately, as is proper, as is right, by right, by rights, condignly, correctly, deservedly, disinterestedly, dispassionately, duly, equally, equitably, evenly, fair, fairly, fittingly, impartially, impersonally, in all conscience, in reason, inequity, injustice, justifiably, justifiedly, justly, meetly, properly, right, rightly, upon even terms, warrantably, warrantedly, without distinction

For further exploring for "rightfully" in Webster Dictionary Online

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