A new design of a cryogenic germanium detector for dark matter search is presented, taking advantage of the coplanar grid technique of event localisation for improved background discrimination. Experiments performed with prototype devices in the EDELWEISS II setup at the Modane underground facility attest to the high efficiency of these devices for p and gamma background rejection. This opens the road to investigate the 10(-8) pb range of WIMP-nucleon collision cross-sections, and possibly beyond, as proposed in the EURECA project of a one-ton Ge detector mass.