Silver-sheathed Bi–Pb–Sr–Ca–Cu–O (2223) superconducting tapes (with a starting composition of Bi1.8Pb0.4Sr2Ca1Cu2O8, calcium cuprate, and CuO) were fabricated by the powder-in-tube technique. The tapes were sintered at various temperatures to optimize the formation of Bi1.8Pb0.4Sr2Ca2Cu3O10 phase within the tape. The results show that sintering within the temperature range of 815–825 °C can produce tapes with high critical current density (Jc). The Jc of samples sintered at the higher temperature of 825 °C, where more liquid is present, depended markedly on the rate at which tapes were cooled from the sintering temperature; samples sintered at lower temperatures did not exhibit such a cooling-rate effect. The optimum combination of phase purity and microstructure that yielded an average transport Jc of ≥ 2.5 × 104 A/cm2 was obtained when the tapes were sintered at 825 °C for 150 h and cooled at a rate of 25 °C/h from the sintering temperature. Quenching studies indicate that the Bi-2223 phase becomes unstable below 700 °C during slow cooling. This result may have important implications for processing Bi–Sr–Ca–Cu–O tapes with high Jc. Addition of 15 vol.% Ag flakes to the monolithic core exerted no significant effect on Jc.