The invention disclosed is a composition of a single-phase solid solution of LiMnO2 and LiMO3 having a Li2MnO3-type crystallographic structure and the general formula Lii+y/3Mn2y/3M(1−y)O2, wherein 0<y<1, manganese is in the 4+ oxidation state, M is one or more transition metal or other cations which have an appropriate ionic radii to be inserted into the structure without unduly disrupting it, but not solely Ni or Cr, e.g. one or more the first row transition metals: Ti, V, Cr, Mn, Fe, Co, Ni or Cu, or other specific other cations: Al, Mg, Mo, W, Ta, Si, Sn, Zr, Be, Ca, Ga, and P, and M has an average oxidation state of +3. Also disclosed are compositions and structures of the materials e.g in the form of a positive electrode for a non-aqueous lithium cell or battery.