  We simplify the classification of supersymmetric solutions with compact
holonomy of the Killing spinor equations of heterotic supergravity using the
field equations and the additional assumption that the 3-form flux is closed.
We determine all the fractions of supersymmetry that the solutions preserve and
find that there is a restriction on the number of supersymmetries which depends
on the isometry group of the background. We examine the geometry of spacetime
in all cases. We find that the supersymmetric solutions of heterotic
supergravity are associated with a large number of geometric structures which
include 7-dimensional manifolds with $G_2$ structure,
  6-dimensional complex and almost complex manifolds, and 4-dimensional
hyper-K\"ahler, K\"ahler and anti-self-dual Weyl manifolds.
