We investigate a scenario with two four branes embedded in six dimensions.
When the metric is periodic and compact in one of the dimensions parallel t
o the branes, the value of the effective cosmological constant for the rema
ining five dimensions can assume a variety of values, determined by the dep
endence of the metric on the sixth dimension. The picture that emerges rese
mbles the Randall-Sundrum model but with an extra warped dimension that all
ows the usual brane-bulk fine tuning to be satisfied without finely tuning
any of the parameters in the underlying six-dimensional theory. Although th
e action contains terms with four derivatives of the metric, we show that w
hen the branes have a finite, natural thickness, such terms have only a sma
ll effect on the Randall-Sundrum structure. The presence of these four deri
vative terms also allows a configuration that resembles that produced by a
domain wall but which results from gravity alone.