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We develop a cross-layer design which combines adaptive modulation and coding (AMC) at the physical layer with a truncated automatic repeat request (ARQ) protocol at the data link layer, in order to maximize spectral efficiency under prescribed delay and performance constraints. We derive the achieved spectral efficiency in closed-form for transmissions over Nakagami-m block fading channels. Numerical results reveal that retransmissions at the data link layer alleviate stringent error-control requirements at the physical layer, and thereby enable considerable spectral efficiency gains. Diminishing returns appear on the spectral efficiency improvement as the number of retransmissions increases, which suggests that a small number of retransmissions strikes a desirable delay-throughput tradeoff.