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 $\cal CPT$-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 $r\to 0$ of the Dirac hyperfine operator, such that the
resulting extended operator can be used nonperturbatively. The binding
correction to magnetic moments is mentioned.