  We propose a new approach to the question of prescribing Gaussian curvature
on the 2-sphere with at least three conical singularities and angles less than
$2\pi$, the main result being sufficient conditions for a positive function of
class at least $C^2$ to be the Gaussian curvature of such a conformal conical
metric on the round sphere. Our methods particularly differ from the
variational approach in that they don't rely on the Moser-Trudinger inequality.
Along the way, we also prove a general precompactness theorem for compact
Riemann surfaces with at least three conical singularities and angles less than
2$\pi$.
