In this paper, the random key pre-distribution scheme introduced in ACM CCS'02 by Eschenauer and Gligor is reexamined, and a generalized form of key establishment is introduced. As the communication overhead is one of the most critical constraints of any successful protocol design, we introduce an alternative scheme in which the connectivity is maintained at the same level as in the original work, while the communication overhead is reduced by about 40% of the original overhead, for various carefully chosen parameters. The main modification relies on the use of a two-level key pool design and two round assignment/key establishment phases. Further analysis demonstrates the efficiency of our modification.