  We present a search for the decays B -> tau nu and B -> K nu nubar in a 253
fb^-1 data sample collected at the Upsilon(4S) resonance with the Belle
detector at the KEKB asymmetric energy B factory. Combinatorial and continuum
backgrounds are suppressed by selecting a sample of events with one fully
reconstructed B. The decay products of the B on the other side of the event are
analyzed to search for B -> tau nu and B -> K nu nubar decays. We find no
significant evidence for a signal and set 90% confidence level upper limits of
B(B -> tau nu) < 1.8*10^-4 and B(B -> K nu nubar) < 3.6*10^-5.
