The present invention generally relates to singly-terminated polyisobutylene (PIB) compounds, and to a process for making such compounds. In one embodiment, the present invention relates to singly-terminated polyisobutylene compounds that contain only one primary alcohol, amine, or methacrylate group as the single-terminating group. In another embodiment, the present invention relates to singly-terminated polyisobutylenes carrying exactly one terminal alcohol, amine, or methacrylate group, where such singly-terminated polyisobutylenes have a number average molecular weight of about 500 to about 5000 grams per mole. In still another embodiment, the present invention relates to singly-terminated polyisobutylene compounds that can be used to synthesize polyurethanes, to polyurethane compounds made via the use of such polyisobutylene compounds, and to processes for making such compounds.