All of the ordinary hyperfine terms of the ipixp) ,L = 1, ortho, bound state, except for the muon-proton contact term, are evaluated to sufficient accuracy so that they would not mask a hyperfine discrepancy associated with proton structure effects. These and other pertinent contributions to the hyperfine structure are discussed in the light of recent interest in checking for a discrepancy in the hyperfine structure of a muon-proton system.