  We consider a class of Einstein-Maxwell-Dilaton theories, in which the
dilaton coupling to the Maxwell field is not the usual single exponential
function, but one with a stationary point. The theories admit two charged black
holes: one is the Reissner-Nordstr{\o}m (RN) black hole and the other has a
varying dilaton. For a given charge, the new black hole in the extremal limit
has the same AdS$_2\times$Sphere near-horizon geometry as the RN black hole,
but it carries larger mass. We then introduce some scalar potentials and obtain
exact charged AdS black holes. We also generalize the results to black
$p$-branes with scalar hair.
