Detailed spectroscopic studies of metal-poor halo stars have highlighted the important role of carbon-enhanced metal-poor (CEMP) stars in understanding the early production and ejection of carbon in the Galaxy and in identifying the progenitors of the CEMP stars among the first stars formed after the Big Bang. Our aim is to determine the frequency and orbital parameters of binary systems among the CEMP-s stars, which exhibit strong enhancements of neutron-capture elements associated with the s-process. We have systematically monitored the radial velocities of a sample of 22 CEMP-s stars for several years with ~monthly, high-resolution, low S/N echelle spectra obtained at the Nordic Optical Telescope (NOT) at La Palma, Spain. From these spectra, radial velocities with an accuracy of ~100 m s-1 were determined by cross-correlation with optimised templates. The conventional scenario of local mass transfer from a former asymptotic giant branch (AGB) binary companion does appear to account for the chemical composition of most CEMP-s stars.