  We report improved measurements of B decays with an eta meson in the final
state using 357 fb^-1 of data collected by the Belle detector at the KEKB e^+
e^- collider. We observe the decays B^+- ->eta pi^+- and B^+- -> eta K^+-; the
measured branching fractions are Br(B^+- -> eta pi^+-) = (3.9 +-
0.5(stat.)+-0.2(sys.))*10^-6 and Br(B^+- -> eta K^+-) =
(2.2+-0.4(stat.)+-0.1(sys.))*10^-6, respectively. Their corresponding
CP-violating asymmetries are measured to be -0.10+-0.11(stat.)+-0.02(sys.) for
eta pi^+- and -0.55+-0.19(stat.)+0.04-0.03(sys.) for eta K^+-. No significant
signal is found for B^0-> eta K^0 decays; the upper limit on the branching
fraction at the 90% confidence level is Br(B^0->eta K^0) < 1.9*10^-6.
