Stimulated Raman Adiabatic Passage (STIRAP) is a method developed more than two decades ago for population transfer in Lambda-type atoms using lasers, with the aim of avoiding an intermediate noisy level. Due to the advantages of being robust, simple, and efficient, STIRAP and its theoretical extensions have found a large variety of applications in atomic and molecular physics, chemistry, as well as quantum information processing. Most recently, the coherent control of solid-state devices has led to remarkable demonstrations of STIRAP with superconducting qubits, optomechanical systems, and NV centers. However, differently from atomic systems, most solid-state quantum devices suffer significant dissipation, thus the prolonged operation time of STIRAP (required by adiabaticity) becomes a severe drawback. In order to provide physical insight and understand the ultimate power of STIRAP, we have pursued an analytical treatment with full consideration of system dissipation. We find that optimizing the transfer time rather than coupling profiles leads to a significant improvement of the transfer fidelity. The upper bound of the fidelity has been found as a simple function of system cooperativities. We also provide a systematic approach to reach this upper bound efficiently. By including the dissipation of all the parties, our results are widely applicable to quantum state engineering and are particularly relevant for solid-state devices.