Narrow-band injection locking of a discharge driven HgBr (

) laser with

(FWHM) < 0.02 cm
-1(

Å) is reported. For injection fluxes as low as 3.3 W/cm
2(

cm
-1), approximately 80 percent of the laser output Was in this band. These results and previous work are analyzed in terms of a Simple Fokker-Planck diffusion model of the HgBr

rotational manifold.