  We present the results of searches for B decays to charmless two-body final
states containing $\eta^\prime$ or $\omega$ mesons, based on 20.7 fb$^{-1}$ of
data collected with the BABAR detector. We find the branching fractions ${\cal
B}(B^+\to\eta^\prime K^+) = (70\pm 8\pm 5)\times 10^{-6}$, ${\cal
B}(B^0\to\eta^\prime K^0) = (42^{+13}_{-11}\pm 4)\times 10^{-6}$, and ${\cal
B}(B^+\to\omega\pi^+)=6.6^{+2.1}_{-1.8}\pm 0.7)\times 10^{-6}$ where the first
error quoted is statistical and the second systematic. We give measurements of
four additional modes for which the 90% confidence level upper limits are
${\cal B}(B^0\to\omega K^0) < 13\times 10^{-6}$, ${\cal B}(B^+\to\eta^\prime
\pi^+) < 12\times 10^{-6}$, ${\cal B}(B^+\to \omega K^+) < 4\times 10^{-6}$,
and ${\cal B}(B^0\to\omega\pi^0) < 3\times 10^{-6}$.
