We introduce a novel hybrid failure model, which facilitates an accurate and detailed analysis of round-based synchronous, partially synchronous and asynchronous distributed algorithms under both process and link failures. Granting every process in the system up to f_\ell send and receive link failures (with f_\ell ^a arbitrary faulty ones among those) in every round, without being considered faulty, we show that the well-known randomized Byzantine agreement algorithm of (Srikanth & Toueg 1987) needs just n \geqslant 4f_\ell + 2f_\ell ^a + 3f_a + 1 processes for coping with f_a Byzantine faulty processes. The probability of disagreement after R iterations is only 2^{ - R}, which is the same as in the FLP model and thus much smaller than the lower bound 0(1/R) known for synchronous systems with lossy links. Moreover, we show that 2-stubborn links are sufficient for this algorithm. Hence, contrasting widespread belief, a perfect communications subsystem is not required for efficiently solving randomized Byzantine agreement.