Rydberg states of the potassium dimer in the 28 430–29 080 cm−1 and 30 030–30 500 cm−1 regions above the ground state X1Σ+g minimum have been studied using the perturbation facilitated optical–optical double resonance technique (PFOODR). Energy levels in these energy regions have been assigned to both triplet and singlet gerade states based on excitation pattern information as well as intensity considerations. Resolved fluorescence from a mixed triplet–singlet 43Πg ∼1Πg upper state to the ground triplet state a 3Σ+u has been used to construct a potential energy curve for the a 3Σ+u state which is in excellent agreement with recent theoretical results. Since this electronic state and the ground singlet state X1Σ+g share the same dissociation limit, we have determined the dissociation energy for the potassium dimer to be De=4450±2 cm−1.