We consider coordinate descent methods for minimization of convex quadratic functions, in which exact line searches are performed at each iteration. (This algorithm is identical to Gauss-Seidel on the equivalent symmetric positive definite linear system.) We describe a class of convex quadratic functions for which the random permutations version of cyclic coordinate descent (RPCD) is observed to outperform the standard cyclic coordinate descent (CCD) approach on computational tests, yielding convergence behavior similar to the fully random variant (RCD). A convergence analysis is developed to explain the empirical observations.