The recently developed effective Schrodinger-like Hamiltonian equation (EHA) in a model space of near-degenerate nonrelativistic two-component spinors is applied to the relativistic energy corrections at first, second, and third order of c(-2) within the framework of relativistic direct perturbation theory (DPT). The dominant singular part of the total relativistic correction is already recovered by the lowest-order effective Hamiltonian in the spirit of degenerate perturbation theory, while the perturbative expansion needs to account for only the small remaining part. Numerical results for groups of excited potential curves of the one-electron H-2(+)-like quasimolecule Sn-2(99+) are presented and discussed. In general the most efficient approach is first-order EHA-DPT for the set of states, followed by single-state DPT of higher orders.