Liquid medicaments incorporate about 1.0-3.0% active benzoyl peroxide (BP) by weight in substantially fully solubilized form, while being substantially free of acetone and other harsh, dermatologically undesirable solvents. The novel compositions are produced by (a) creating an emulsion or slurry of BP in an emollient, topically acceptable ester, and (b) dissolving the emulsion or slurry in absolute alcohol. The medicaments may be used in the treatment of BP-responsive skin conditions in mammals, e.g., acne vulgaris or rosacea. The novel medicaments may be dispensed directly to the affected skin area through the use of an applicator device comprising a fluid reservoir associated with a foam applicator tip, or via a spray dispenser, atomizer or pump spray.