Infrared-absorption lines of the (X,Y) and Z local modes of hydrogenic C4v centres in rare-earth doped CaF2 and SrF2 have differing 10K linewidths, attributed in part to one-phonon decay from the upper to the lower frequency local mode. However for SrF2 the lower frequency (Z) mode has the larger line width for Gd3+, Tb3+ and Dy3+ and one-phonon decay cannot be the primary cause for the differing line widths. This is borne out by free-electron laser 10K studies of the H-lines in SrF2:0.33%Gd3+, which yield (X,Y) and Z mode lifetimes of 43 and 30 ps suggesting similar homogeneous linewidths. The larger line-width for the Z mode is attributed to the greater sensitivity of this mode to rare-earth ion mismatch and to crystal disorder.