The present disclosure provides methods for identifying therapeutic agents that are multifunctional radical quenchers. It also provides compounds of formula (I), (II), or (II-A): and pharmaceutically acceptable salts thereof, compositions comprising these compounds, and methods of using these compounds in a variety of applications, such as treatment or suppression of diseases associated with decreased mitochondrial function resulting in diminished ATP production and/or oxidative stress and/or lipid peroxidation.