Substantial improvements have been made in the sensitivity of an ac susceptibility measurement system which determines the pressure dependence of the superconducting transition temperature, T(c)(P). The pressure, P, is determined near T(c) from the position of the R1 and R2 fluorescence peaks from ruby chips. The system was used to determine T(c)(P) for several high T(c) single crystals, but was not sufficiently sensitive to determine T(c)(P) of polycrystalline samples for HgBa2CuO4+delta. 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, T(c)(P) of HgBa2CuO4+delta polycrystal to 4 GPa is presented. The improvement of the system using the diamond anvil cell opens the possibility of measuring T(c) above 10 GPa and on smaller samples.