CDMS II data from the 5-tower runs at the Soudan Underground Laboratory were reprocessed with an improved charge-pulse fitting algorithm. Two new analysis techniques to reject surface-event backgrounds were applied to the 612 kg days germanium-detector WIMP-search exposure. An extended analysis was also completed by decreasing the 10 keV analysis threshold to $sim$5 keV, to increase sensitivity near a WIMP mass of 8 GeV/$c^2$. After unblinding, there were zero candidate events above a deposited energy of 10 keV and 6 events in the lower-threshold analysis. This yielded minimum WIMP-nucleon spin-independent scattering cross-section limits of $1.8 times 10^{-44}$ and $1.18 times 10 ^{-41}$ cm$^2$ at 90% confidence for 60 and 8.6 GeV/$c^2$ WIMPs, respectively. This improves the previous CDMS II result by a factor of 2.4 (2.7) for 60 (8.6) GeV/$c^2$ WIMPs.
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