The two electrons of a Cooper pair in a conventional superconductor form a spin singlet and therefore a maximally entangled state. Recently, it was demonstrated that the two particles can be extracted from the superconductor into two spatially separated contacts via two quantum dots in a process called Cooper pair splitting (CPS). Competing transport processes, however, limit the efficiency of this process. Here we demonstrate efficiencies up to 90%, significantly larger than required to demonstrate interaction-dominated CPS, and on the right order to test Bell's inequality with electrons. We compare the CPS currents through both quantum dots, for which large apparent discrepancies are possible. The latter we explain intuitively and in a semiclassical master equation model. Large efficiencies are required to detect electron entanglement and for prospective electronics-based quantum information technologies.