Substantial improvements have been made in the sensitivity of an ac susceptibility measurement system which determines the pressure dependence of the superconducting transition temperature,Tc(P). The pressure,P, is determined nearTcfrom the position of theR1andR2fluorescence peaks from ruby chips. The system was used to determineTc(P) for several highTcsingle crystals, but was not sufficiently sensitive to determineTc(P) of polycrystalline samples for HgBa2CuO4+&dgr;. This motivated us to improve the sensitivity of our system. Other parts of the system and the data analysis procedures also have been improved. As a demonstration,Tc(P) of HgBa2CuO4+&dgr;polycrystal to 4 GPa is presented. The improvement of the system using the diamond anvil cell opens the possibility of measuringTcabove 10 GPa and on smaller samples.