A disposable absorbent pant having an enhanced belted or balloon-type structure is disclosed. The belt structure may be formed of stretch laminate material, including laterally pre-strained elastomeric material sandwiched between inner and outer layers of nonwoven web material. The belt structure may include one or more unelasticized zones, in which the elastomeric material is omitted, removed or deactivated. As a result, lateral gathers or ruffles of the inner and outer layers, otherwise resulting from elastic contraction of the pre-strained elastomeric material, are substantially reduced in size and/or frequency, or eliminated, within the unelasticized zones. The laminate in the unelasticized zone(s) will thus have relatively lower z-direction thickness and will lie more closely against the wearer's skin. When unelasticized zone(s) are located proximate the sides/hip areas of the product, for example, this effect may provide the product with a more tailored profile and enhance its discreetness when worn beneath outer clothing.