High-quality electron beams, with a few 109 electrons within a few percent of the same energy above 80 MeV, were produced in a laser wakefield accelerator by matching the acceleration length to the length over which electrons were accelerated and outran (dephased from) the wake. A plasma channel guided the drive laser over long distances, resulting in production of the high-energy, high-quality beams. Unchanneled experiments varying the length of the target plasma indicated that the high-quality bunches are produced near the dephasing length and demonstrated that channel guiding was more stable and efficient than relativistic self-guiding. Consistent with these data, particle-in-cell simulations indicate production of high-quality electron beams when trapping of an initial bunch of electrons suppresses further injection by loading the wake. The injected electron bunch is then compressed in energy by dephasing, when the front of the bunch begins to decelerate while the tail is still accelerated.