Optimum compositions that lead to (Tl1-xPbx)(Sr1.6Ba0.4)Ca2Cu3Ag0.4Oy (referred to as Tl,Pb-1223) phase evolution have been identified. The Tl-free precursor powders with the composition Sr1.6Ba0.4Ca2Cu3Ag0.4O7 were prepared in an aerosol flow reactor. These precursor-powders were then mixed with appropriate amounts of Tl2O3 and PbO, pressed and wrapped in a gold foil, and introduced into a furnace kept at 920 degrees C where they were held at 920 degrees C for 2 hours before being slow cooled to room temperature in 4-5 hours under flowing oxygen. X-ray data showed that single-phase Tl,Pb-1223 can be obtained in the range x = 0.3-0.5. All the samples studied were found to be superconducting. The T-c (diamagnetic onset) for Tl,Pb-1223 single phase varies from 105 K to 116 K for the as-synthesized samples.