  Using a sample of 3.7 x 10^6$ Upsilon(4S) -> B Bbar events collected with the
BaBar detector at the PEP-II storage ring, we search for the electroweak
penguin decays B+ -> K+ e+ e-, B+ -> K+ mu+ mu-, B0 -> K*0 e+ e-, and B0 -> K*0
mu+ mu-. We observe no significant signals for these modes and set preliminary
90% C.L. upper limits of Br(B+ -> K+ e+ e-) < 12.5 x 10^(-6), Br(B+ -> K+ mu+
mu-) < 8.3 x 10^(-6), Br(B0 -> K*0 e+ e-) < 24.1 x 10^(-6), and Br(B0 -> K*0
mu+ mu-) < 24.5 x 10^(-6).
