We present searches for the leptonic decays B+→ℓ+ν and the lepton flavor violating decays B0→ℓ±τ, where ℓ=e, μ, with data collected by the BABAR experiment at SLAC. This search demonstrates a novel technique in which we fully reconstruct the accompanying B̄ in Υ(4S)→BB̄ events, and look for a monoenergetic lepton from the signal B decay. The signal yield is extracted from a fit to the signal lepton candidate momentum distribution in the signal B rest frame. Using a data sample of approximately 378×106 BB̄ pairs (342fb-1), we find no evidence of signal in any of the decay modes. Branching fraction upper limits of B(B+→e+ν)<5.2×10-6, B(B+→μ+ν)<5.6×10-6, B(B0→e+τ-)<2.8×10-5 and B(B0→μ+τ-)<2. 2×10-5, are obtained at 90% confidence level. © 2008 The American Physical Society.