Motivated by the low-jitter requirements of streaming multi-media traffic, we focus on the development of scheduling strategies under fading conditions that not only maximize throughput performance but also provide regular inter-service times to users. Since the service regularity of the traffic is related to the higher-order statistics of the arrival process and the policy operation, it is highly challenging to characterize and analyze directly. We overcome this obstacle by introducing a new quantity, namely the time-since-last-service, which has a unique evolution different from a tradition queue. By combining it with the queue-length in the weight, we propose a novel maximum-weight type scheduling policy that is proven to be throughput-optimal and also provides provable service regularity guarantees. In particular, our algorithm can achieve a degree of service regularity within a constant factor of a fundamental lower bound we derive. This constant is independent of the higher-order statistics of the arrival process and can be as low as two. Our results, both analytical and numerical, exhibit significant service regularity improvements over the traditional throughput-optimal policies, which reveals the importance of incorporating the metric of time-since-last-service into the scheduling policy for providing regulated service.