We present a formalisation of a category of schemes that we refer to as broadcast-enhanced key predistribution schemes (BEKPSs). These schemes are suitable for networks with access to a trusted base station and an authenticated broadcast channel. We demonstrate that the access to these extra resources allows for the creation of BEKPSs with advantages over key predistribution schemes such as flexibility and more efficient revocation. There are many possible ways to implement BEKPSs, and we propose a framework for describing and analysing them. In their paper “From Key Predistribution to Key Redistribution,” Cichoń et al. [2010] propose a scheme for “redistributing” keys to a wireless sensor network using a broadcast channel after an initial key predistribution. We classify this as a BEKPS and analyse it in that context. We provide simpler proofs of some results from their paper, give a precise analysis of the resilience of their scheme, and discuss possible modifications. We then study two scenarios where BEKPSs may be particularly desirable and propose a suitable family of BEKPSs for each case. We demonstrate that they are practical and efficient to implement, and our analysis shows their effectiveness in achieving suitable trade-offs between the conflicting priorities in resource-constrained networks.