Edelweiss is a weakly interacting massive particle (WIMP) direct detection experiment using 320 g ionization-heat cryogenic Ge detectors operated in the very low-background environment of the Frejus Underground Laboratory (French Alps). Edelweiss has presently the best sensitivity for all WIMPs with a mass greater than 35 GeV. For these ionization-heat Ge detectors, the rejection of incomplete charge collection events represents the main challenge. New results on the rejection power of our detectors will be presented. On the other hand, detectors design has been studied to reduce the energy threshold and then to be more sensitive to WIMP interactions. (C) 2003 Elsevier Science B.V. All rights reserved.