Key predistribution is a well-known technique for ensuring secure communication via encryption among sensors deployed in an ad-hoc manner to form a sensor network. In this paper, we propose a novel 2-Phase technique for key predistribution based on a combination of inherited and random key assignments from the given key pool to individual sensor nodes. We also develop an analytical framework for measuring security-performance tradeoffs of different key distribution schemes by providing metrics for measuring sensornet connectivity and resiliency to enemy attacks. In particular, we show analytically that the 2-Phase scheme provides better average connectivity and superior $q$-composite connectivity than the random scheme. We then prove that the invulnerability of a communication link under arbitrary number of node captures by an adversary is higher under the 2-Phase scheme. The probability of a communicating node pair having an exclusive key also scales better with network size under the 2-Phase scheme. We also show analytically that the vulnerability of an arbitrary communication link in the sensornet to single node capture is lower under 2-Phase assuming both network-wide as well as localized capture. Simulation results also show that the number of exclusive keys shared between any two nodes is higher while the number of $q$-composite links compromised when a given number of nodes are captured by the enemy is smaller under the 2-Phase scheme as compared to the random one.