We introduce and analyze various approaches for computing excited electronic states using our recently developed adaptive configuration interaction (ACI) method [ Schriber , J. B. and Evangelista , F. A. J. Chem. Phys. 2016 , 144 , 161106 ]. These ACI methods aim to describe multiple electronic states with equal accuracy, including challenging cases like multielectron, charge-transfer, and near-degenerate states. We develop both state-averaged and state-specific approaches to compute excited states whose absolute energy error can be tuned by a user-specified energy error threshold, σ. State-averaged schemes are found to be more efficient in that they obtain all of the states simultaneously in one computation, but they lose some degree of statewise tunability. State-specific algorithms allow for direct control of the error of each state, though the states must be computed sequentially. We compare each method using methylene, LiF, and all-trans polyene benchmark data.