Experimental and computational studies have revealed that T-cell cross-reactivity is a widespread phenomenon that can either be advantageous or detrimental to the host. In particular, detrimental effects can occur whenever the clonal dominance of memory cells is not justified by their infection-clearing capacity. Using an agent-based model of the immune system, we recently predicted the "memory anti-naïve" phenomenon, which occurs when the secondary challenge is similar but not identical to the primary stimulation. In this case, the pre-existing memory cells formed during the primary infection may be rapidly deployed in spite of their low affinity and can actually prevent a potentially higher affinity naïve response from emerging, resulting in impaired viral clearance. This finding allowed us to propose a mechanistic explanation for the concept of "antigenic sin" originally described in the context of the humoral response. However, the fact that antigenic sin is a relatively rare occurrence suggests the existence of evolutionary mechanisms that can mitigate the effect of the memory anti-naïve phenomenon. In this study we use computer modeling to further elucidate clonal dominance and the memory anti-naïve phenomenon, and to investigate a possible mitigating factor called attrition. Attrition has been described in the experimental and computational literature as a combination of competition for space and apoptosis of lymphocytes via type-I interferon in the early stages of a viral infection. This study systematically explores the relationship between clonal dominance and the mechanism of attrition. Our results suggest that attrition can indeed mitigate the memory anti-naïve effect by enabling the emergence of a diverse, higher affinity naïve response against the secondary challenge. In conclusion, modeling attrition allows us to shed light on the nature of clonal interaction and dominance.