Both the Chevrel phase compound EuMo//6S//8 and the organic material, (TMTSF)//2FSO//3 are superconducting only under moderate pressure. In both instances the absence of superconductivity at ambient pressure is directly attributed to a low temperature structural distortion that introduces a gap over all or part of the Fermi surface. The role of pressure is to suppress the transition and thus allow the electrons to condense into the superconducting state. In EuMo//6S//8, details of the pressure dependence of both the structural and superconducting transition have been explained on the basis of a competition between a charge density wave-type state and superconductivity. In the case of (TMTSF)//2FSO//3 an anion ordering giving rise to a metal-insulator transition is responsible for suppressing superconductivity.