This paper investigates the problem of secret key generation over a wiretap channel when the terminals observe correlated sources. These sources may or may not be independent of the main channel and the users overhear them before the transmission takes place. A novel achievable scheme for the case of independent sources is proposed, and it is shown to be optimal under certain less noisy conditions. This result improves upon the existing literature where the more stringent condition of degradedness was needed. For the situation where the sources are correlated with the main channel, a second achievable scheme based on joint source-channel coding is introduced, for which special cases of binary and Gaussian channels are studied. Some optimality results are derived, however, these are much less general than for the first setup.