It is not easy to achieve secure key establishment in wireless sensor networks without public key cryptography. Many key management protocols have been proposed for the purpose. Among them, LEAP is a simple and elegant protocol that establishes multi-level keys in an efficient way, but its security mainly relies on that of a single initialization key. Though it is assumed that the initial deployment phase is secure and the key is erased from sensor nodes after the initialization in LEAP, the assumption could not be viable for two reasons. First, the same key should be used again for node addition after the initialization phase whereas the new node can be captured before removing the key. Second, the initial deployment of dense networks may not take short as LEAP expected in many cases. This paper rethinks the security of LEAP and proposes a more secure scheme with a new notion of probabilistic time intervals. Rather we localize the impact of key compromise within the time intervals.