content is at least 30% by weight and up to 65% by weight, up to 55% by weight or up to 50% by weight. In preferred embodiments in which the only isocyanate -reactive compounds are polyols b-1) and b-2), the hard segment content is equal to: An advantage of the invention is that metallic and amine urethane catalysts are not necessary and can be omitted. In some embodiments, therefore, the polyurethane (and the prepolymer or quasi-prepolymer, if prepared) is made in the substantial absence of such a urethane catalyst. In particular embodiments, the reaction mixture in each of the reaction steps, as well as the polyurethane reaction product, contains no more than 20 parts by weight per million parts by weight reaction mixture (ppm) of zinc, tin and mercury combined and more preferably no more than 10 ppm or 5 ppm thereof, and no more than 0.1 weight percent, no more than 0.05 weight percent or no more than 0.025 weight percent, based on the weight of the reaction mixture, of amine group- containing compounds that have molecular weights below 350 (other than the alkoxylated Mannich base described herein). In such embodiments, the reaction mixture may contain no more than 0.1 weight percent, no more than 0.05 weight percent or no more than 0.025 weight percent, based on the weight of the reaction mixture, of any amine group-containing compounds other than the alkoxylated Mannich. In other particular embodiments, the reaction mixture in each of the various reaction steps preferably contains no more than 20 ppm of metals and more preferably no more than 10 ppm or 5 ppm thereof, and in addition contains no more than 0.1 weight percent, no more than 0.05 weight percent or no more than 0.025 weight percent of amine group-containing compounds that have molecular weights of below 350 other than the alkoxylated Mannich base. In such other particular embodiments, the reaction mixture may contain no more than 0.1 weight percent, no more than 0.05 weight percent or no more than 0.025 weight percent, based on the weight of the reaction mixture, of any amine group-containing compounds other than the alkoxylated Mannich base. The polyurethane of the invention preferably contains correspondingly low amounts of such metals and such low molecular weight, non-isocyanate-reactive amine group-containing compounds. The polyurethane has a density of at least 750 kg/m $^{3}$, preferably 900 kg/m $^{3}$, and more preferably at least 1000 kg/m$^{3}$. It is preferably non-cellular or