The majority of security systems for wireless sensor networks are based on symmetric encryption. The main open issue for these approaches concerns the establishment of symmetric keys. A promising key distribution technique is the random predistribution of secret keys. Despite its effectiveness, this approach presents considerable memory overheads, in contrast with the limited resources of wireless sensor networks. In this paper, an in-depth analytical study is conducted on the state-of-the-art key distribution schemes based on random predistribution. A new protocol, called $q$ - $s$ - composite , is proposed in order to exploit the best features of random predistribution and to improve it with lower requirements. The main novelties of $ q$ - $ s$ -composite are represented by the organization of the secret material that allows a storing reduction, by the proposed technique for pairwise key generation, and by the limited number of predistributed keys used in the generation of a pairwise key. A comparative analysis demonstrates that the proposed approach provides a higher level of security than the state-of-the-art schemes.