  We consider compactifications of heterotic supergravity on anti-de Sitter
space, with a six-dimensional nearly K"ahler manifold as the internal space.
Completing the model proposed by Frey and Lippert with the particular choice of
SU(3)/U(1)xU(1) for the internal manifold, we show that it satisfies not only
the supersymmetry constraints but also the equations of motion with string
corrections of order alpha'. Furthermore, we present a non-supersymmetric
model. In both solutions we find confirmed a recent result of Ivanov on the
connection used for anomaly cancellation. Interestingly, the volume of the
internal space is fixed by the supersymmetry constraints and/or the equations
of motion.
