  The coronal magnetic field directly or indirectly affects a majority of the
phenomena studied in space physics. It provides energy for coronal heating,
controls the release of coronal mass ejections (CMEs), and drives heliospheric
and magnetospheric activity, yet the coronal magnetic field itself has proven
difficult to measure. This difficulty has prompted a decades-long effort to
develop accurate, timely, models of the field - an effort that continues today.
We have developed a method for improving global coronal magnetic field models
by incorporating the type of morphological constraints which could be derived
from coronal images. Here we report promising initial tests of this approach on
two theoretical problems, and discuss opportunities for application.
