  We consider an extension of a special class of conformal sigma models
(`chiral null models') which describe extreme supersymmetric string solutions.
The new models contain both `left' and `right' vector couplings and should
correspond to non-BPS backgrounds. In particular, we discuss a conformal
six-dimensional model which is a combination of fundamental string and 5-brane
models with two extra couplings representing rotations in orthogonal planes. If
the two rotational parameters are independent the resulting background is found
to be either singular or not asymptotically flat. The non asymptotically flat
solution has a regular short distance limit described by a `twisted' product of
SL(2,R) and SU(2) WZW theories with two twist parameters mixing the isometric
Euler angles of SU(2) with a null direction of SL(2,R).
