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In this paper, we investigate the roles of cooperative jamming (CJ) and noise forwarding (NF) in improving the achievable secrecy rates of a Gaussian wiretap channel (GWT). In particular, we study the role of a deaf helper in confusing the eavesdropper in a GWT channel by either transmitting white Gaussian noise (cooperative jamming) or by transmitting a dummy codeword of no context yet drawn from a codebook known to both the destination and the eavesdropper (noise forwarding). We first derive the conditions under which each mode of deaf cooperation improves over the secrecy capacity of the original wiretap channel and show that a helping node can be either a useful cooperative jammer or a useful noise forwarder but not both at the same time. Secondly, we derive the optimal power allocation for both the source and the helping node to be used in each of the two modes of deaf helping. Thirdly, we consider the deaf helper selection problem where there are N relays present in the system and it is required to select the best K deaf helpers, K ≥ 1, that yield the maximum possible achievable secrecy rate. For the case of K=1, we give the optimal selection strategy with optimal power allocation. The computational complexity of the optimal selection strategy when K > 1 is relatively large, especially for large values of K and N. Thus, we propose a suboptimal strategy for the selection problem when K > 1. We derive the complexity of the proposed selection strategies and show that, for K > 1, our suboptimal strategy, which works in a greedy fashion, enjoys a significantly less computational complexity than the optimal strategy. Nevertheless, as demonstrated by numerical examples, our suboptimal strategy gives rise to reasonable performance gains in terms of the achievable secrecy rate with respect to the case of K=1.