Effect of pressure on hole-doped CeCoIn$_{5}$ and CeRhIn$_{5}$.*

With one less p-electron than In, Cd or Hg adds one hole per substituted In in CeMIn$_{5}$ (M=Co,Rh, Ir). Progressive Cd/Hg substitutions tune the ground state of superconducting CeCoIn$_{5}$ to one of coexisting magnetism and superconductivity and eventually to antiferromagnetic only. This systematic evolution of states in doped CeCoIn$_{5}$ is reversed accurately by applied pressure and maps onto the temperature-pressure phase diagram of pure CeRhIn$_{5}$. These observations, together with the response of Cd-substituted CeRhIn$_{5}$ to applied pressure, show that ground states of CeMIn$_{5}$ are controlled by fine details of electronic structure and that disorder on the In site and different ionic radii of Cd and Hg have an insignificant effect.