Three new potassium rare-earth/titanium phosphate structures, K(2)ErTi(PO(4))(3) (KErTP), K(2)YbTi(PO(4))(3) (KYbTP) and K(2)YTi(PO(4))(3) (KYTP), are presented, all of which are characterized by single-crystal X-ray diffraction studies. In addition, a fourth structure, K(2)CrTi(PO(4))(3) (KCrTP), has been reinvestigated. All structures are isostructural to the langbeinite-type structure and result from changes made to the growth constituents in high-temperature flux-growth experiments intended to give structurally modified potassium titanyl phosphate (KTP). The two crystallographically independent octahedra sites (site symmetry 3) have a mixed Ti/M (M = Er, Yb, Y or Cr) population, although the rare-earth metals favour one site while chromium favours the other. An alternative approach for the description of the channels and cation cages in langbeinite and related structures is given using [M(5)X(6)O(39)] units. The framework of langbeinite is compared with that of nasicon using these alternative building units. All of the investigated structures crystallize in space group P2(1)3 with Z = 4; a = 10.1053 (2) A, R = 0.023 (KErTP); a = 10.0939 (8) A, R = 0.022 (KYbTP); a = 10.1318 (6) A, R = 0.047 (KYTP); a = 9.8001 (2) A, R = 0.016 (KCrTP).