CPT-invariant two-fermion Dirac equation with extended hyperfine operator

For the S-states of muonium and positronium, the hyperfine shifts to the order alpha(6) of a recently derived two-fermion equation with explicit CPT-invariance are checked against the results of a nonrelativistic reduction, and the leading alpha(8) shifts are calculated. An additional hyperfine operator is discovered which can milden the singularity for r --> 0 of the Dirac hyperfine operator, such that the resulting extended operator may be used nonperturbatively. A binding correction to magnetic moments is derived from CPT-invariance.