  We report recent results in the search for the rare B meson decays B-->rho
gamma and B0-->pi0 pi0. These results are based on 56.4 1/fb collected by the
BaBar Collaboration at the SLAC PEP-II e+e- B Factory. We set new 90%
confidence level upper limits BR(B0 --> rho0 gamma) < 1.5 x 10^-6, BR(B+ -->
rho+ gamma) < 2.8 x 10^-6, and BR(B0 --> pi0 pi0) < 3.4 x 10^-6.
