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Use of a so-called two-powder process results in rapid formation of a highly pure superconducting bismuth-2223 phase during powder-in-tube processing. In this process, Sr_χCa_1−χCuO₂ and Bi_1.8Pb_0.4Sr_2−χCa_1+χCu₂O₈ are formed as separate intermediate phases, and mixed, then processed together within a silver sheath. Mixtures with χ values of 0.0, 0.25, 0.50, 0.75, and 1.0 are studied in order to probe the relationship between 2223 formation and the melting behavior of 2212. The best results to date have been obtained with the χ=0.0 mixture containing high-melting, strontium-rich 2212 and calcium cuprate. The process is very reproducible and produces nearly pure 2223 in as little as 50 h.