Topical compositions are provided that have 0.5% or more of at least one personal care or pharmaceutical acid, and lightly- to moderately-crosslinked PVP, which is an effective thickener in the low pH systems. In preferred embodiments, the acid is a hydroxy acid and the composition used for personal care, or prescriptive or non-prescriptive medication indications for use on the skin, hair, scalp, foot, or lips. Also provided is the use of the topical compositions to deliver the acid(s) to the skin, hair, scalp, foot, or lips. Especially preferred is a use to reduce irritation and stinging compared to an equivalent compositions not having lightly- to moderately-crosslinked PVP.