The transport critical current density (J_c) of silver-sheathed polycrystalline Bi(Pb)-Sr-Ca-Cu-O (BPSCCO) tapes has been measured at approximately 10 K intervals from 4.2 K up to 77 K in fields of 1-20 T. The tapes were produced by swaging, drawing and multiple final pressing and sintering steps, which developed a preferred orientation of the basal planes of the predominantly 2223 BPSCCO phase within the tape J_c values greater than 10⁴ A cm^-2 at 4.2 K were obtained, and these decreased smoothly as the field and temperature were increased. No evidence of any catastrophic change in J_c(H) was seen at any temperature, thus suggesting that flux line lattice melting is not controlling the J_c of these tapes.