A method proposed some time ago to correct for residual correlation effects within the framework of equation-of-motion coupled-cluster theory for ionized states in the singles and doubles approximation (EOMIP-CCSD) is discussed, and a minor modification is suggested that provides a more balanced theoretical treatment. The resulting approach is used to calculate properties of diatomic radicals, where comparison with experiment and other high-level calculations is straightforward. In addition, two electronic states of NO2 and the ground state of the cyclic C3H molecule are studied, cases in which symmetry-breaking phenomena play an important role. Results indicate that EOMIP-CCSD* generally provides a systematic improvement relative to the uncorrected EOMIP-CCSD approach for predicting properties of radicals.