Key pre-distribution (KPD) schemes, which are inherently trade-offs between security and complexity, are perhaps well suited for securing large-scale deployments of resource constrained nodes without persistent access to a trusted authority (TA). However, the need to offset their inherent security limitations, calls for some degree of tamper-resistance of nodes. Obviously, if absolute tamper-resistance is guaranteed, KPD schemes are rendered secure. In practice, however, tamper-resistance will have some limitations which will be exploited by attackers. In this paper, we analyze the security of deployments of random key pre-distribution schemes based on some assumptions on the "extent of tamper-resistance." We argue that a "limited extent of tamper resistance" when used in conjunction with a mechanism for "periodic key updates," drastically improves the security of (especially random) KPD schemes.