Compact and preferably cellular polyurethane elastomers are produced by reacting a) polyhydroxyl compounds having molecular weights of from 800 to 6000 and, if desired, b) chain extenders and/or crosslinkers having molecular weights of up to 800 [lacuna] c) naphthylene 1,5-diisocyanate and at least one additional aromatic diisocyanate selected from the group consisting of tolylene diisocyanate, diphenylmethane diisocyanate, 3,3'-dimethylbiphenyl diisocyanate, 1,2-diphenylethane diisocyanate and phenylene diisocyanate, and/or aliphatic diisocyanate having from 4 to 12 carbon atoms and/or cycloaliphatic diisocyanate having from 6 to 18 carbon atoms, where the formative components (a), (c) and, if used, (b) are preferably reacted by the prepolymer method, in the presence or absence of d) catalysts, e) blowing agents and f) additives. Isocyanate prepolymers suitable for this purpose are also described.