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Background Individual T-cells differ in phenotype, reflecting their cellular state, and in genotype (clonotype), determined by genetic variation at the T-cell receptor (TCR) loci. T-cell clones vary by number and quality, with some clones more effective due to higher-quality TCR interactions. Selecting clones that optimally interact with and recognize their target is important for cellular immunotherapies. Tumor-specific but mildly-effective T-cells can confound this selection.Methods To identify optimal T-cell clones, we modeled different immune-response scenarios by extending a CAR-T competition model using ordinary differential equations (ODEs). Scenarios varied the proportion of less-capable clones occupying the finite carrying capacity of T-cells. Model parameters for clone quality and carrying capacity were derived from an earlier CAR-T cell model of T-cell competition.Results Our model predicts that when mildly-effective clones dominate the T-cell response, their lower killing efficacy prevents tumor clearance. Removing these clones restores effective anti-tumor activity. Our model recapitulates in vivo studies and elegantly describes previously disparate immunological failures.Conclusions With finite T-cell capacity, selective removal of ineffective and mildy-effective clones explains the benefit of immunodepletion and underscores that autologous T-cells must be both antigen-specific and highly potent.