In a sample of 6.6 x 10(6) produced B mesons we have observed decays B
--> eta'K, with branching fractions B(B+ --> eta'K+)= (6.5(-1.4)(+1.5
) +/- 0.9) X 10(-5) and B(B-0 --> eta'K-0) = (4.7(-2.0)(+2.7) +/- 0.9)
X 10(-5). We have searched with comparable sensitivity for 17 related
decays to final states containing an eta or eta' meson accompanied by
a single particle or low-lying resonance. Our upper limits for these
constrain theoretical interpretations of the B --> eta'K signal.