Résumé : In this report, variants are proposed to the Defect Correction algorithm analyzed for hyperbolic equations in \cite{DESIH} \cite{HDESI}. Potentially more efficient preconditioners are identified for a class of second-order partially-upwind approximation schemes including one that is third-order; these preconditioners are constructed by averaging the first-order upwind operator with the central-difference operator. Additionally, it is shown that the implicit equations can be solved by relaxation; for this purpose, a 3-stage iterative algorithm is proposed.