  We examine several different types of five dimensional stationary spacetimes
with bulk scalar fields and parallel 3-branes. We study different methods for
avoiding the appearance of spacetime singularities in the bulk for models with
and without cosmological expansion. For non-expanding models, we demonstrate
that in general the Randall-Sundrum warp factor is recovered in the asymptotic
bulk region, although elsewhere the warping may be steeper than exponential. We
show that nonsingular expanding models can be constructed as long as the
gradient of the bulk scalar field vanishes at zeros of the warp factor, which
are then analogous to the particle horizons found in expanding models with a
pure AdS bulk. Since the branes in these models are stabilized by bulk scalar
fields, we expect there to be no linearly unstable radion modes. As an
application, we find a specific class of expanding, stationary solutions with
no singularities in the bulk in which the four dimensional cosmological
constant and mass hierarchy are naturally very small.
