We present a single-determinant approach to three challenging topics in the chemistry of excited states: double excitations, charge-transfer states, and conical intersections. The results are obtained by using the Initial Maximum Overlap Method (IMOM) which is a modified version of the Maximum Overlap Method (MOM). The new algorithm converges better than the original, especially for these difficult problems. By considering several case studies, we show that a single-determinant framework provides a simple and accurate alternative for modeling excited states in cases where other low-cost methods, such as CIS and TD-DFT, either perform poorly or fail completely.