When a quantum dot is attached to a metallic reservoir and a superconducting contact Andreev processes leads to a finite subgap current at the normal lead and the creation or destruction of Cooper pairs. Andreev-reflection engines profit from the destruction of Cooper pairs to provide the work needed to set a charge current at the normal-conductor contact generating electrical power. For this power-transduction device high power and large efficiencies in quantum-mechanically enhanced regimes are demonstrated. There thermodynamic trade-off relations between power, efficiency and stability, valid for any classical engine are overcome, and kinetic constraints on the engine precision are largely surpassed in arbitrary far from equilibrium conditions.