  We report new results from the Cryogenic Dark Matter Search (CDMS II) at the
Soudan Underground Laboratory. Two towers, each consisting of six detectors,
were operated for 74.5 live days, giving spectrum-weighted exposures of 34 kg-d
for germanium and 12 kg-d for silicon targets after cuts, averaged over recoil
energies 10-100 keV for a WIMP mass of 60 GeV. A blind analysis was conducted,
incorporating improved techniques for rejecting surface events. No WIMP signal
exceeding expected backgrounds was observed. When combined with our previous
results from Soudan, the 90% C.L. upper limit on the spin-independent
WIMP-nucleon cross section is 1.6 x 10^{-43} cm^2 from Ge, and 3 x 10^{-42}
cm^2 from Si, for a WIMP mass of 60 GeV. The combined limit from Ge (Si) is a
factor of 2.5 (10) lower than our previous results, and constrains predictions
of supersymmetric models.
