Disclosed are anhydrous antiperspirant and deodorant compositions that comprise from about 0.1% to about 30% by weight of an antiperspirant or deodorant active; from about 0.01% to about 20% by weight of a solid, water-soluble Vitamin B3 material; from about 0.1% to about 40% by weight of a suspending agent; from about 0.1% to about 2.0% by weight of glycerin; and from about 10% to about 99% by weight of an anhydrous carrier liquid other than and in addition to the glycerin. The anhydrous compositions have lower visible residue on the applied areas of the skin even though they also contain relatively high residue solids in the form of solid, water-soluble, Vitamin B3 materials. The compositions also provide for a dry, silky feeling during or after application.