How to enhance the superconducting critical temperature (Tc) has been a primary issue since the discovery of superconductivity. The highest Tc reported so far is 166 K in HgBa2Ca2Cu3O8+δ (Hg1223) at high pressure of 23 GPa, as determined with the reduction onset, but not zero, of resistivity. To clarify the possible condition of the real maximum Tc, it is worth revisiting the effects of pressure on Tc in the highest Tc family. Here we report a systematic study of the pressure dependence of Tc in HgBa2CaCu2O6+δ (Hg1212) and Hg1223 with the doping level from underdoped to overdoped. The Tc with zero resistivity is probed with a cubic-anvil-type apparatus that can produce hydrostatic pressures. Variation, not only increase but also decrease, of Tc in Hg1212 and Hg1223 with pressure strongly depends on the initial doping levels. In particular, we confirm a maximum Tc of 153 K at 22 GPa in slightly underdoped Hg1223.