We use numerical simulations to investigate the effects of photodarkening (PD) on pulse compression and coherent combination following chirped-pulse amplification in Yb-doped fiber amplifiers. Even though we increase the pump power to keep the pulse energy constant, PD degrades the pulses due to phase distortions resulting from heating acting already within a pulse as well as to increased self-phase modulation if the fiber length is optimized for the PD-free fiber at beginning of life. By contrast, in a fiber shorter than this, the drop in peak power is a relatively modest 35% even at a PD propagation loss as large as 5 dB, thus providing effective mitigation against PD-induced phase distortions. The improvements extend to the combination efficiency of beam-combined systems.