For the first singlet excited states C 1 Π of IIIA group monohalides GaCl, GaBr, InCl, and InBr, a very shallow potential well may exist in the flat potential energy curve, which poses a challenge to the theoretical accuracy. In this study, high-level theoretical calculations have been performed through the Feller-Peterson-Dixon composite approach to study the C 1 Π states, and the obtained spectroscopic constants agree well with the known experimental ones. It is found that the C 1 Π states are sensitive to the size of basis functions, spin−orbit coupling, and strong correlations mainly due to triple excitations. The final results show that the C 1 Π states of GaCl and InCl are quasi-bound with one (v′ = 0) and four (v′ = 0−3) vibrational levels, respectively, being consistent with the experimental findings, whereas the C 1 Π states of GaBr and InBr are repulsive. Our conclusions deny the existence of higher vibrational levels v′ = 1 for GaCl, v′ > 3 for InCl, and v′ ≥ 0 for InBr in previous experimental and theoretical studies of C 1 Π.