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CDMS II data from the five-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 weakly interacting massive particle (WIMP)-search exposure. An extended analysis was also completed by decreasing the 10 keV analysis threshold to ~5 keV, to increase sensitivity near a WIMP mass of 8 GeV/c2. After unblinding, there were zero candidate events above a deposited energy of 10 keV and six events in the lower-threshold analysis. This yielded minimum WIMP-nucleon spin-independent scattering cross-section limits of 1.8x10-44 and 1.18x10-41 at 90% confidence for 60 and 8.6 GeV/c2 WIMPs, respectively. This improves the previous CDMS II result by a factor of 2.4 (2.7) for 60 (8.6) GeV/c2 WIMPs.