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tokens: inclination, i , must be specified during the starspot modelling and line profile recovery. The stellar radius cannot generally be measured directly from observation, which means that i is not generally known. We performed a 2 search for a range of stellar axial inclinations, i rec , to determine the effect of an incorrectly determined axial inclination. A minimum 2 is always attained at the simulated combination of v sin i and P rot , irrespective of adopted axial inclination for 30 i rec 90. These parameters are therefore effectively independent of the choice of i rec . However, for the trial i rec values, only 2percent r.m.s. variation in was seen, with no discernible trend in 2 versus i rec in the 3090 range above the scatter. Thus, although the simulated inclination of i 60 cannot be recovered for v sin i = 5km s 1 , this does not preclude identification of v sin i and P rot , which are correctly recovered at all trial i rec values. A robustly determined rotation period, P rot and v sin i still enable i to be estimated for an assumed stellar radius. The typical 10percent uncertainty for M dwarf estimates of R (Stassun etal. 2012 ; Williams etal. 2015 ) will dominate uncertainty in the axial inclination determination. For instance, uncertainties of 10percent in sin i yield , , , and (upper limits at 75 and 90 arise from requiring sin i 1). For RV sim data using i 60 and N obs = 60, Fig. 3 (right) shows the FAP for RV corr data points using i 3090 (in 15 steps). In fact, there is a tendency towards improved FAPs when using higher inclinations (i.e. i rec = 75 and 90) for recovery. This is likely related to the lack of resolution elements, when instrumental resolution and stellar v sin i are of comparable magnitude. 4 SENSITIVITIES As every object and data set combination is unique, a full exploration of parameter space is beyond the scope of this paper. Nevertheless, a more complete picture of the range of sensitivities can be gained by exploring the S/N and v sin i values that are expected empirically. Fig. 5 shows the reduction in starspot noise achieved, = sim / corr (where sim and corr are the r.m.s. for the RV sim and RV corr data points), as a function of v sin i for the simulated S/N ratios. The lowest values of are found for Model 2, where 1. Again, this is due to an inability to recover the small spots, and in some combinations, the noise may be marginally increased by5percent. The procedure is most efficient for v sin i 5 km s 1 , where a maximum 8.6 is achieved. At v sin i 1km s 1 , the efficiency is generally lower, as fitting distortions below the instrumental resolution is less effective. For v sin i 10km s 1 , although starspot distortions are modelled well, the broader lines due to higher v sin i limit the efficiency of the procedure by increasing the RV uncertainties. Figure 5. Starspot noise reduction factor, , as a function of v sin i for S/N = 2000, 5000 and 10000 (bottom to top). For projected equatorial rotation