We both theoretically and experimentally investigate the optimization of femtosecond Yb-doped fiber amplifiers (YDFAs) to achieve high-quality, high-power, compressed pulses. Ultrashort pulses amplified inside YDFAs are modeled by the generalized nonlinear Schrödinger equation coupled to the steady-state propagation-rate equations. We use this model to study the dependence of compressed-pulse quality on the YDFA parameters, such as the gain fiber's doping concentration and length, and input pulse pre-chirp, duration, and power. The modeling results confirmed by experiments show that an optimum negative pre-chirp for the input pulse exists to achieve the best compression.