Experiments performed with the high-contrast 0.7-J 35-fs Ti:sapphire laser at the Lund Laser Centre focused into a helium gas jet have produced quasi-monoenergetic electron beams with energies up to 150 MeV. The beam is produced as a result of controlled wavebreaking of a wakefleld generated by the relativistically channeled laser beam. Under the best conditions of laser energy and plasma density, a beam with narrow-energy-spread component was produced on every shot with an energy stability of ~10% and a pointing stability of ~6 mrad. Furthermore, it can be deduced that the electron beam originates from a source with both transverse and longitudinal extents < 10 mum, implying a pulselength of < 25 fs. These measurements mark an important improvement in the characterization, as well as repeatability, of laser-plasma-generated electron beams with a single driver laser beam.