High-quality Bi-2212 ceramic samples were obtained by a solid-state reaction method. At the starting composition Bi2.12Sr1.90Ca1.02Cu1.96Oy, X-ray diffraction, optical micrographs and scanning electron microscopy investigations show that the level of impurity phases is less than 1% by volume. Synthesis at a few degrees below the melting point favours grain growth. A final annealing treatment at controlled temperature and oxygen pressure, followed by rapid quenching, yields sharp superconducting transitions, as observed by measurement of the a.c. susceptibility and Meissner effect, and specific heat experiments. The Meissner fraction in 2 mT approaches 50%.