Continuous, broad, and single-mode wavelength tuning of thermoelectrically cooled short-pulse quantum-cascade lasers is demonstrated with a combination of coarse grating tuning and fine phase tuning of the gain element. This approach overcomes the problem of a poor facet antireflection coating of the gain chip by shifting a Fabry-Perot longitudinal mode to coincide with the desired grating-selected wavelength. The 9-microm laser was tested with NH3 gas absorption and showed fine frequency tuning at a rate of 31 MHz/step and a time-averaged linewidth of 500-750 MHz. The total tuning range was 9.08-9.36 microm and was limited only by the intrinsic gain of the device.