  We have searched a sample of 9.6 million BBbar events for the flavor-changing
neutral current decays B -> K l^+ l^- and B -> K^*(892) l^+ l^-. We subject the
latter decay to the requirement that the dilepton mass exceed 0.5 GeV. There is
no indication of a signal. We obtain the 90% confidence level upper limits on
the branching fractions Br(B -> K l^+ l^-) < 1.7 \times 10^{-6} and Br(B ->
K^*(892) l^+ l^-) < 3.3 \times 10^{-6}. We also obtain an upper limit on the
weighted average 0.65 Br(B -> K l^+ l^-) + 0.35 Br(B -> K^*(892) l^+ l^-) < 1.5
\times 10^{-6}. The weighted-average limit is only 50% above the Standard Model
prediction.
