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In the LEAP framework for wireless sensor networks a set of keys is used to secure communication. LEAP distinguishes between unicast (pairwise) communication, group (cluster) communication and global (broadcast) communication. The keys used in pairwise communication are derived from an initial key Kj that nodes are equipped with prior to deployment and that is deleted after link setup. Further keys are distributed encrypted with these pairwise keys. It is a weakness that, if the initial key is ever disclosed, the whole network is compromised. To lower the threat of Kj disclosure, we present a Kj-less scheme for key predistribution. Our scheme is based on random key predistribution, and proves to perform better in medium sized networks than previous proposals. It is resilient against node capture attacks and allows node to node authentication. Attacks against overlying protocols in the network are more difficult with this scheme. We have conducted computations to show the feasibility of our scheme for networks up to a size of 1000 nodes. By introducing a key reuse system we are able to increase the probability of a successful link setup. We have included a security analysis that discusses our scheme's resistance against commonly known attacks.