  A new family of five dimensional, R=0 braneworlds with asymmetric warp
factors is proposed. Beginning with the invariance of the Ricci scalar for the
general class of asymmetrically warped spacetimes we, subsequently specialise
to the R=0 case. Solutions are obtained by choosing a particular relation
(involving a parameter $\nu$) between the warp factors. Symmetric warping
arises as a special case (particular value of $\nu$). Over a range of values of
$\nu$ the energy conditions for the matter stress energy are found to hold
good. It turns out that the energy density and pressures required to support
these spacetimes decay as the inverse square of the fifth (extra) coordinate.
The projection of this bulk stress--energy (for symmetric warping) on the
3--brane yields an effective cosmological constant. We conclude with brief
comments on spacetimes with constant Ricci scalar and the extension of our
results to diverse dimensions.
