  We report results from high resolution optical spectroscopy of three
non-radiative galactic supernova remnants, RCW 86, Kepler's supernova remnant
and SN 1006. We have measured the narrow component H-alpha line widths in
Balmer-dominated filaments in RCW 86 and SN 1006, as well as the narrow
component width in a Balmer-dominated knot in Kepler's SNR. The narrow
component line widths measured in RCW 86 and Kepler's SNR show FWHM of 30-40
km/s, similar to what has been seen in other Balmer-dominated remnants. Of the
remnants in our sample, SN 1006 is the fastest shock (~3000 km/s). The narrow
component H-alpha and H-beta lines in this remnant have a FWHM of merely 21
km/s. Comparing the narrow component widths measured in our sample with those
measured in other remnants shows that the width of the narrow component does
not correlate in a simple way with the shock velocity. The implications for the
pre-heating mechanism responsible for the observed line widths are discussed.
