Strongly overdoped HgBa 2 Ca 2 Cu 3 O 8ϩ␦ ͑Hg-1223͒ samples with superconducting transitions as low as 97 K were successfully obtained by using HgO, Ca 2 CuO 3 , CuO, and mixtures of highly oxidized BaCuO 2ϩ⑀ (⑀ Ϸ0.13) and/or BaO 2 powders as starting materials for the high-pressure synthesis at 5 GPa and 950°C. The overdoped state was confirmed by observing negative values for the Seebeck coefficient throughout the temperature range from T c to 320 K in a thermoelectric power measurement. Also, both of the cell parameters a and c were found to decrease with decreasing T c , reflecting, respectively, an increase in hole concentration in the CuO 2 planes and the incorporation of oxygen into the HgO ␦ layer. The oxygen excess ␦ as determined by the Cu͑ϩI͒/Cu͑ϩII͒ coulometric titration method, was ϳ0.19 in the overdoped sample with T c ϭ107 K. Subsequent reducing annealing in an Ar atmosphere at 280°C increased the T c to 131 K. Consistently, only positive Seebeck coefficient values were observed up to 320 K for the Ar-annealed sample. A clearly underdoped material with T c ϭ118 K was obtained by annealing the same sample in Ar at a higher temperature (ϳ400°C). Finally, high-pressure synthesis starting from less-oxidized BaCuO 2ϩ⑀ (⑀Ϸ0.06) yielded a Hg-1223 material with ␦Ϸ0.10 and T c ϭ132 K. ͓S0163-1829͑97͒04945-X͔