  We present the results of a search for the rare decays $B\to
h\nu\overline{\nu}$, where $h$ stands for $K^+,\:K^0_{\mathrm{S}},\:K^{\ast
+},\:K^{\ast 0},\:\pi^+,\:\pi^0,\:\rho^+$ and $\rho^{0}$. The results are
obtained with $772\times10^{6}$ $B\overline{B}$ pairs collected with the Belle
detector at the KEKB $e^+ e^-$ collider. We reconstruct one $B$ meson in a
semileptonic decay and require a single $h$ meson but nothing else on the
signal side. We observe no significant signal and set upper limits on the
branching fractions. The limits set on the $B\to
K^0_{\mathrm{S}}\nu\overline{\nu}$, $B^0\to K^{*0}\nu\overline{\nu}$, $B\to
\pi^+\nu\overline{\nu}$, $B^0\to\pi^0\nu\overline{\nu}$,
$B^+\to\rho^+\nu\overline{\nu}$, and $B^0\to\rho^0\nu\overline{\nu}$ channels
are the world's most stringent.
