  We report results of a search for $B\to\tau\nu$ in a sample of 9.7 million
charged $B$ meson decays. The search uses both $\pi\nu$ and $\ell\nu\bar\nu$
decay modes of the $\tau$, and demands exclusive reconstruction of the
companion $\bar B$ decay to suppress background. We set an upper limit on the
branching fraction ${\cal B}(B\to \tau\nu) < 8.4\times 10^{-4}$ at 90%
confidence level. With slight modification to the analysis we also establish
${\cal B}(B^\pm\to K^\pm\nu\bar\nu) < 2.4\times 10^{-4}$ at 90% confidence
level.
