The tunabilities of both the wavelength and the pulse width of monolithic mode-locked semiconductor lasers are demonstrated for the first time. Pulses shorter than 1.6 ps, tunable over 8.8 nm, have been generated by a temperature-tuned monolithic colliding pulse mode-locked (CPM) quantum-well laser. For a fixed wavelength, the pulse width is independently controlled from 1.2 ps to longer than 3 ps by external bandpass filters. Near transform-limited time-bandwidth products of 0.34 are maintained throughout the tuning processes.