  We present a new method that incorporates the horizontal branch morphology
into synthetic colour-magnitude diagram based star formation history
determinations. This method, we call MORGOTH, self-consistently takes into
account all the stellar evolution phases up to the early asymptothic giant
branch, flexibly modelling red giant branch mass loss. We test MORGOTH on a
range of synthetic populations, and find that the inclusion of the horizontal
branch significantly increases the precision of the resulting star formation
histories. When the main sequence turn-off is detected, MORGOTH can fit the
star formation history and the red giant branch mass loss at the same time,
efficiently breaking this degeneracy. As part of testing MORGOTH, we also model
the observed colour-magnitude diagram of the well studied Sculptor dwarf
spheroidal galaxy. We recover a new more detailed star formation history for
this galaxy. Both the new star formation history and the red giant branch mass
loss we determined for Sculptor with MORGOTH are in good agreement with
previous analyses, thus demonstrating the power of this new approach.
