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Density down-ramp (DDR) injection is a promising concept in beam-driven plasma wakefield accelerators for the generation of high-quality witness beams. We review and complement the theoretical principles of the method and employ particle-in-cell (PIC) simulations in order to determine constrains on the geometry of the density ramp and the current of the drive beam, regarding the applicability of DDR injection. Furthermore, PIC simulations are utilized to find optimized conditions for the production of high-quality beams. We find and explain the intriguing result that the injection of an increased charge by means of a steepened ramp favors the generation of beams with lower emittance. Exploiting this fact enables the production of beams with high charge (∼140  pC), low normalized emittance (∼200  nm) and low uncorrelated energy spread (0.3%) in sufficiently steep ramps even for drive beams with moderate peak current (∼2.5  kA).