New powder synthesis methods have been developed for the preparation of single-phase TI2CaBa2Cu2Oa (the 2122 compound) and T12Ca2Ba2Cu3Oto (the 2223 compound) powders from stoichiometric reactant mixtures. The 2122 compound was prepared from a stoichiometric mixture of T1203, CuO and CaBa2CuO4, while the 2223 compound was prepared from the same mixture hut with additional CaO and CuO to match the correct (TI:Ca:Ba:Cu = 2:2:2:3 ) stoichiometry. For the 2122 compound, XRD single-phase samples with zero-resistivity temperatures (Tยข.ze~o) above 100 K were obtained by using a one-step calcination at 830ยฐC for a period between 6 and 23 h. A maximum of To.zero of 116 K was obtained for 14h of calcination. For the 2223 compound, XRD single-phase samples with Tยข.z,~o between 110 and 118 K were obtained by employing a two-step calcination procedure consisting of a first calcination at 830ยฐC for 5 h and a second calcination at 870ยฐC for a period between 2 and 6 h. Both the 2122 and 2223 samples thus prepared exhibit sharp superconducting transitions and typically have a saturation Meissner effect of about 20% of ( -1/4n) under a field of 20 G. Powder melting is completely eliminated during the preparation of the 2122 compound and much reduced, by employing the pre-calcination step, during the preparation of the 2223 compound. Compared with the conventional method, the new methods require less stringent calcination conditions, and hence allow for a better process control of the synthesis of T12CanBa2Cun+106+n superconducting powders.