We study the state-dependent (SD) wiretap channel (WTC) with non-causal channel state information (CSI) at the encoder. This model subsumes all other instances of CSI availability as special cases, and calls for an efficient utilization of the state sequence both for reliability and security purposes. A lower bound on the secrecy-capacity, that improves upon the previously best known result by Chen and Han Vinck, is derived based on a novel superposition coding scheme. An example in which the proposed scheme achieves strictly higher rates is provided. Specializing the lower bound to the case where CSI is also available to the decoder reveals that the lower bound is at least as good as the achievable formula by Chia and El-Gamal, which is already known to outperform the adaptation of the Chen and Han Vinck code to the encoder and decoder CSI scenario. Our achievability gives rise to the exact secrecy-capacity characterization of a class of SD-WTCs that decompose into a product of two WTCs, one is independent of the state and the other one depends only on it. The results are derived under the strict semantic-security metric that requires negligible information leakage for all message distributions. The proof of achievability relies on a stronger version of the soft-covering lemma for superposition codes.