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We construct an analytic self-map $\Phi$ of the bidisk ${\mathbb D}^2$ whoseimage touches the distinguished boundary, but whose approximation numbers ofthe associated composition operator on $H^2 ({\mathbb D}^2)$ are small in thesense that $\limsup_{n \to \infty} [a_{n^2} (C_\Phi)]^{1 / n} < 1$.

An extremal composition operator on the Hardy space of the bidisk with small approximation numbers