  Accounting for stellar activity is a crucial component of the search for
ever-smaller planets orbiting stars of all spectral types. We use Doppler
imaging methods to demonstrate that starspot induced radial velocity
variability can be effectively reduced for moderately rotating, fully
convective stars. Using starspot distributions extrapolated from sunspot
observations, we adopt typical M dwarf starspot distributions with low contrast
spots to synthesise line profile distortions. The distortions are recovered
using maximum entropy regularised fitting and the corresponding stellar radial
velocities are measured. The procedure is demonstrated for a late-M star
harbouring an orbiting planet in the habitable zone. The technique is effective
for stars with vsini = 1-10 km/s, reducing the stellar noise contribution by
factors of nearly an order of magnitude. With a carefully chosen observing
strategy, the technique can be used to determine the stellar rotation period
and is robust to uncertainties such as unknown stellar inclination. While
demonstrated for late-type M stars, the procedure is applicable to all spectral
types.
