The paper treats several ordering principles for the solution of Poisson- type elliptic boundary value problems with preconditioned conjugate gradient methods (PCG). As preconditioners SSOR and incomplete Cholesky (IC) are considered. For the solution of the relevant linear systems, which mostly are tridiagonal, on vector or parallel computers multicolor orderings exhibit a high degree of parallelism, but on the other hand the convergence of the PCG may suffer from them. The author starts his consideration with diagonal ordering, which produces the same updating as natural ordering such that no difference in convergence can occur. He then discusses in detail the generalizations of diagonal ordering (reverse Cuthill-McKee and domain decomposition ordering) and the influence of the ordering principles to vector lengths and parallelization. The typical 2D and 3D stencils are considered. The influence of the ordering on the condition number of the preconditioned matrix and on the rate of convergence is studied. There is a connection of this rate to the number of nonzero elements in the remainder matrix which can be estimated. Earlier results of other authors can be explained in this way. The considerations are restricted to rectangular or parallelepiped domains and Dirichlet boundary conditions.