  We study supersymmetric compactification to four dimensions with non-zero
H-flux in heterotic string theory. The background metric is generically
conformally balanced and can be conformally Kahler if the primitive part of the
H-flux vanishes. Analyzing the linearized variational equations, we write down
necessary conditions for the existence of moduli associated with the metric. In
a heterotic model that is dual to a IIB compactification on an orientifold, we
find the metric moduli in a fixed H-flux background via duality and check that
they satisfy the required conditions. We also discuss expressing the conditions
for moduli in a fixed flux background using twisted differential operators.
