A composition of matter that may be used to make transparent, substantially gel-free polymeric films includes at least a styrenic block copolymer and a thermoplastic resin other than the styrenic block copolymer. The styrenic block copolymer (e.g. S-I-B-S) has four distinct and sequential blocks: a first styrenic block (S), a first diene block (e.g. isoprene or I), a second diene block that differs from the first diene block (e.g. butadiene or B) and a second styrenic block (S). The styrenic block copolymer desirably lacks any random diene block (e.g. a random isoprene/butadiene block). The styrenic block copolymer also desirably lacks any significant percentage of a triblock copolymer (S-I-B). The composition of matter may also include an extender material such as white mineral oil. The compositions may be used to make mono-layer or multi-layer cast or blown films.