The superconducting transition temperatures (Tc's) of optimally doped HgBa2Cam-1CumO2m+2+δ (Hg 1:2:m-1:m) with m=1, 2, and 3 and Hg1-xPbxBa2Ca2Cu3O8+δ [Hg(xPb) 1:2:2:3] have been investigated resistively under quasihydrostatic pressures up to 45 GPa. There seems to be a universal upward shift of Tc under pressure, regardless of m, for all Hg 1:2:m-1:m, implying a common origin for all compounds. Record high Tc's of 164, 154, and 118 K were reached for the optimally doped Hg 1:2:m-1:m with m=3, 2, and 1, respectively. However, the Tc enhancement is suppressed by Pb substitution, suggesting the possibility that Hg plays an important role in these compounds.
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