Recovery of data packets from packet erasures in a timely manner is critical for many streaming applications. An early paper by Martinian and Sundberg introduced a framework for streaming codes and designed rate-optimal codes that permit delay-constrained recovery from an erasure burst of length up to B. A recent work by Badr et al. extended this result and introduced a sliding-window channel model C(N, B, W). Under this model, in a sliding-window of width W, one of the following erasure patterns are possible (i) a burst of length at most B or (ii) at most N (possibly non-contiguous) arbitrary erasures. Badr et al. obtained a rate upper bound for streaming codes that can recover with a time delay T, from any erasure patterns permissible under the C(N, B, W) model. However, constructions matching the bound were absent, except for a few parameter sets. In this paper, we present a family of codes that achieves the rate upper bound for all feasible parameters N, B, W and T. © 2018 IEEE.