We consider an extension of a special class of conformal sigma models
('chiral null models') which describe extreme supersymmetric string so
lutions. The new models contain both 'left' and 'right' vector couplin
gs and should correspond to non-BPS backgrounds. In particular, we dis
cuss a conformal six-dimensional model which is a combination of funda
mental string and 5-brane models with the two extra couplings represen
ting rotations in the orthogonal planes. If the two rotation parameter
s are independent the resulting background is found to be either singu
lar or non-asymptotically flat. The non-asymptotically flat solution h
as a regular short distance limit described by a 'twisted' product of
SL(2,R) and SU(2) WZW theories with two twist pararmeters mixing the i
sometric Euler angles of SU(2) with a null direction of SL(2,R).