1) Appropriately 2) Aright 3) Completely 4) Deservedly 5) Fairly 6) Justifiedly 7) Justly 8) Right 9) Truthfully 10) Virtuously 1) Justifiedly 2) Justly 3) With honesty 
• (adv.) According to truth or fact; correctly; not erroneously; exactly. • (adv.) Properly; fitly; suitably; appropriately. • (adv.) According to justice; according to the divine will or moral rectitude; uprightly; as, duty rightly performed. • (adv.) Straightly; directly; in front.
Right'ly adverb [ Anglo-Saxon richtlice .] 1. Straightly; directly; in front. [ Obsolete] Shak. 2. According to justice; according to the divine will or moral rectitude; uprightly; as, duty rightly performed. 3. Properly; fitly; suitably; appropriately. ...
[adv] - with honesty
justly 1 justifiedly adverb with honesty; `he was rightly considered the greatest singer of his time`