This paper presents a list of suggested stars for radial velocity measurements. We explain here in brief the research project for which the radial velocity of the "slow movers" i.e. small proper motion stars are necessary. Basing on this study we prepared a list of 1100 stellar targets with very accurate positions, proper motions and trigonometric parallaxes but without radial velocity measurements. Distributions of stellar brightnesses and spectral types among these stars are presented as well as its "most wanted" subset. We announce the begin of the radial velocity measurements to be conducted with our new echelle spectrograph just put into operation and offer some coordination for observations of targets that cannot be reached from our location.