We present orbital amplitude and orbital gradient equations for the quadratic coupled-cluster doubles (QCCD) theory. These expressions are size extensive and can be solved in O(N-6) time with the use of O(N-4) intermediates, which are efficiently defined. The optimized orbital formalism is naturally suited for excitations in only a valence space to describe nondynamical correlation. This also minimizes the additional cost relative to conventional CCD. The resulting valence QCCD is used to study the effects of correlation on equilibrium geometries of a range of small molecules in the perfect pairing active space. This enables comparison with generalized valence bond perfect pairing calculations on the same systems. Additionally, the use of valence QCCD as a supplement to complete active space (CAS) methods is illustrated with calculations of the transition structure for addition of hydrogen to trans-diazene (N2H2).