  We present a new method, the Coupled Escape Probability (CEP), for exact
calculation of line emission from multi-level systems, solving only algebraic
equations for the level populations. The CEP formulation of the classical
two-level problem is a set of {\em linear equations}, and we uncover an exact
analytic expression for the emission from two-level optically thick sources
that holds as long as they are in the "effectively thin" regime. In comparative
study of a number of standard problems, the CEP method outperformed the leading
line transfer methods by substantial margins.
  The algebraic equations employed by our new method are already incorporated
in numerous codes based on the escape probability approximation. All that is
required for an exact solution with these existing codes is to augment the
expression for the escape probability with simple zone-coupling terms. As an
application, we find that standard escape probability calculations generally
produce the correct cooling emission by the CII 158 mic line but not by the
$^3$P lines of OI.
