Previous works have proven that power consumption side-channel attacks, such as the Template Attack and the Stochastic Model, are effective for small secrets, such as those with 8 or 16 bits. However, directly applying those side-channel attacks on systems with large secrets, for example AES 128, is computationally intractable. Attackers usually apply a divide-and-conquer strategy to partition the secret in order to scale to larger numbers of bits. In the case of AES, divide-and-conquer strategy based side-channel attacks are usually launched on either the first round or the last round of the AES encryption. In this paper, we propose an efficient and pragmatic attack strategy that exploits the samples from multiple rounds, which significantly improves the key recovery compared to standard divide-and-conquer strategies.