The 1223 and 1122 structure-types of Tl-Bi-Sr-Ca-Cu-O, with Tc values between 92 K and 87 K, have been analysed by convergent beam electron diffraction and energy-dispersive X-ray analysis (CBED and EDX). The compositional formulae Tl0.8Bi0.4Ca1.0Sr2.0Cu3Oy and Tl0.8Bi0.4Ca0.8Sr1.7Cu2Oy were obtained, with the space group allocations P1 and P2 mm for the 1223 and 1122 compounds, respectivelt. The analysis suggests that Bi substitution for Ca, rather than for Tl, may be the main mechanism responsible for raising the overall positive charge of the lattice. Oxalate co-precipitation of the metal cations from solutions, buffered to control the Cu content, has been used to promote the single-phase formation of the BiCaSrCuO precursors, and hence of the final Tl compounds. In the course of this work, the previously unreported n=5 member of the BiSrCaCuO series was identified, with a Tc value of 92 K being possibly associated with its presence.