The possibility of efficient electron cooling of ion beams with wide velocity spread was investigated experimentally with the storage ring TSR at MPI für Kernphysik in Heidelberg. Two different cooling methods have been studied. The results of the schemes using an induction accelerator (IndAcc) to accelerate the ion beam towards the active region of the cooling force, and the ramping of the velocity of the electron beam through the velocity range of the ion beam by changing the cathode voltage of the electron gun are presented. Both methods were tested with a carbon ion beam 12C6+ with kinetic energy of 73.3 MeV. Significant reduction of the cooling time to 0.65 and 0.35 s are achieved for "induction acceleration sweep" and "electron energy sweep" methods, respectively, compared with 2.8 s for conventional cooling.