This invention relates to rigid polyurethanes prepared by reaction, at an isocyanate index of 95 to 110, of(a) an allophanate-modified aliphatic and/or cycloaliphatic polyisocyanurate;(b) 20 to 100% by weight, relative to the total of components (b) and (c), of(i) one or more polyether and/or polyester polyols containing three or more isocyanate-reactive hydroxyl groups and having a molecular weight of 200 to 6000, and(ii) 0 to 30% by weight, relative to component (b)(i), of one or more isocyanate-reactive compounds other than a polyether or polyester of component (b)(i) and containing two or more isocyanate-reactive hydroxyl groups and having a molecular weight of about 400 to about 10,000,(c) 0 to 30% by weight, relative to the total of components (b) and (c), of a chain extender and/or crosslinker other than a polyether or polyester and having a molecular weight of from 32 to 399, wherein the amounts of components (b) and (c) total 100% by weight.