Anhydrous, solid antiperspirant compositions comprising: (a) from about 0.1% to about 30% by weight of the composition, of a high-efficacy antiperspirant active; (b) from about 0.1% to about 35% by weight of the composition, of a thickening agent; (c) from about 10% to about 99% by weight of the composition, of an anhydrous liquid carrier; (d) from about 5 ppm to about 20% by weight of the composition, of a primary fragrance; and (e) from at least about 5 ppm by weight of the composition, of a secondary fragrance that is distinct from the primary fragrance and is included in a surfactant-free, water-releasable matrix, which renders the secondary fragrance within the matrix substantially odorless prior to aqueous activation, wherein the anhydrous, solid antiperspirant composition exhibits an Antiperspirant Efficacy Index of at least about 0.9, and wherein the anhydrous, solid antiperspirant composition is substantially devoid of a malodor reducing agent.