Preparation of isobutene homopolymers having a weight-average molecular weight of 75 000 to 10 000 000 by polymerization of isobutene, by (a) performing the polymerization at −80° C. to −190° C., (b) using, as an inert solvent, optionally halogenated C1 to C5 hydrocarbons, (c) using, as a polymerization catalyst, a Lewis acid complex, (d) performing the polymerization in the presence of at least one reaction accelerator in the form of an ethylenically saturated hydrocarbon compound comprising one oxygen atom and no abstractable proton, and (e) performing the polymerization in the presence of at least one chain length regulator comprising one tertiary olefinic carbon atom.