Over the years, the Byzantine Generals Problem has become notorious for the complexity of its solutions. This is particularly true for protocols with the early-stopping property. Moreover, minor changes in the fault model resulted in drastically different protocols. In this paper, we expose a fundamental technique that underlies most of these protocols. We then derive a simple, intuitive, failure-model-independent scheme for solving the Byzantine Generals Problem. The derivation reveals when it is possible to stop early. Using this result, we extend the basic framework into one that yields simple, early-stopping protocols for the Eventual Byzantine Agreement problem. We demonstrate the utility of our results by deriving an early-stopping protocol.