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Generalized integrated interleaved (GII) codes can nest BCH sub-codewords to form stronger BCH codewords. They are among the best candidates for error correction in the new storage class memories (SCMs). However, SCMs require short codeword length and low redundancy. In this case, the nested key equation solver (KES), which is a key step in GII decoding, has a small number of iterations. The initialization and/or scalar pre-computation in previous nested KES designs have large area and may take even longer time than the iterations themselves. This paper proposes an efficient nested KES design for short GII-BCH codes. The polynomial updating is decomposed into two steps to reduce the critical path without requiring scalar pre-computation. Besides, the KES is reformulated to reduce the number of clock cycles without incurring any area overhead. For an example code over GF(2^{10}) that protects 2560 bits with 10% redundancy, the proposed design achieves at least 25% area reduction and 37% reduction on the area-time product averaged over the nested decoding rounds compared to prior efforts.