We report first results from the Anglo-Australian Telescope Rocky Planet Search – an intensive , high-precision Doppler planet search targeting low-mass exoplanets in contiguous 48 night observing blocks . On this run we targeted 24 bright , nearby and intrinsically stable Sun-like stars selected from the Anglo-Australian Planet Search ’ s main sample . These observations have already detected one low-mass planet reported elsewhere ( HD 16417b ) , and here we reconfirm the detection of HD 4308b . Further , we have Monte-Carlo simulated the data from this run on a star-by-star basis to produce robust detection constraints . These simulations demonstrate clear differences in the exoplanet detectability functions from star to star due to differences in sampling , data quality and intrinsic stellar stability . They reinforce the importance of star-by-star simulation when interpreting the data from Doppler planet searches . The simulations indicate that for some of our target stars we are sensitive to close-orbiting planets as small as a few Earth masses . The two low-mass planets present in our 24 star sample indicate that the exoplanet minimum mass function at low masses is likely to be a flat \alpha \sim - 1 ( for dN / dM \propto M ^ { \alpha } ) and that between 15 \pm 10 \% ( at \alpha = -0.3 ) and 48 \pm 34 \% ( at \alpha = -1.3 ) of stars host planets with orbital periods of less than 16 days and minimum masses greater than 3 M _ { \oplus } .