During the adaptive immune response, the vertebrate immune system preferentially targets a select handful of amino acid sequences, or epitopes, from hundreds that are presented by the invading pathogen. This extremely focused targeting behavior is known as immunodominance and appears to be critically important in the functioning of the adaptive immune response. Presently, however, immunodominance is a poorly understood natural phenomenon. This paper investigates a class of mathematical models for immunodominance. These models take the form of multivariable optimal control problems with control constraints and free terminal time. Theoretical analysis is conducted to establish singular controls for several cases. For biologically reasonable parameter values, the results indicate that immunodominance is the optimal choice of the immune system.