The Cryogenic Dark Matter Search (CDMS) uses low-temperature Ge and Si detectors to search for Weakly Interacting Massive Particles (WIMPs) via their elastic-scattering interaction with atomic nuclei while discriminating against interactions of background particles. CDMS data from 1998 and 1999 with a relaxed fiducial-volume cut (resulting in 15.8 kg-days exposure on Ge) are consistent with an earlier analysis with a more restrictive fiducial-volume cut. Twenty-three WIMP candidate events are observed, but these events are consistent with a background from neutrons. Resulting limits on the spin-independent WIMP-nucleon elastic-scattering cross-section are lower than those of any other experiment for WIMPs with masses between 10–70 GeV c −2. Under the assumptions of standard WIMP interactions and a standard halo, the results are incompatible with the annual-modulation signal of DAMA at 99.99% CL in the asymptotic limit.