Utilizing AC susceptibility measurements the authors have investigated the inter and intragranular properties of selected bulk materials under hydrostatic pressures to 3.5 GPa. A single phase Tl₂CaBa₂Cu₂O₈ sample with superconducting transition temperature T_c approximately=107 K shows a clear maximum in T_c(P) at approximately 2.2 GPa coupled with a nearly twofold increase to 3 GPa of the intergranular critical current density J_cJ near T_c. The second sample, a YBa₂Cu₄O₈ sinter, shows a large linear increase in T_c with pressure (+5.5 K/GPa) as well as a fivefold increase J_cJ to 3 GPa. Applying a critical state model, the authors find that T_c(P) varies as lambda _g^-2(P), where lambda _g is the intragranular (London) penetration depth.