  This work is part of an ongoing project which aims to detect terrestrial
planets in our neighbouring star system $\alpha$ Centauri using the Doppler
method. Owing to the small angular separation between the two components of the
$\alpha$ Cen AB binary system, the observations will to some extent be
contaminated with light coming from the other star. We are accurately
determining the amount of contamination for every observation by measuring the
relative strengths of the H-$\alpha$ and NaD lines. Furthermore, we have
developed a modified version of a well established Doppler code that is
modelling the observations using two stellar templates simultaneously. With
this method we can significantly reduce the scatter of the radial velocity
measurements due to spectral cross-contamination and hence increase our chances
of detecting the tiny signature caused by potential Earth-mass planets. After
correcting for the contamination we achieve radial velocity precision of $\sim
2.5\,\mathrm{m\,s^{-1}}$ for a given night of observations. We have also
applied this new Doppler code to four southern double-lined spectroscopic
binary systems (HR159, HR913, HR7578, HD181958) and have successfully recovered
radial velocities for both components simultaneously.
