Planetary companions of a fixed mass induce reflex motions with a larger amplitude around lower-mass stars, which adds to making M dwarfs excellent targets for extra-solar planet searches. The most recent velocimeters with a stability of ~1 m ssup -1 can detect very low-mass planets out to the habitable zone of these stars. Low-mass small planets are abundant around M dwarfs, and most of the known potentially habitable planets orbit one of these cool stars. Our M-dwarf radial velocity monitoring with HARPS on the ESO 3.6 m telescope at La Silla observatory makes a major contribution to this sample. We present here dense radial velocity (RV) time series for three M dwarfs observed over ~five years: GJ 3293 (0.42 M ), GJ 3341 (0.47 M ), and GJ 3543 (0.45 M). We extracted these RVs through minimum xsup 2-matching of each spectrum against a stack of all observed spectra for the same star that has a high signal-to-noise ratio.