We present new admission tests for periodic realtime threads with explicitly stated deadlines scheduled according to the earliest deadline first (EDF) algorithm. In traditional real-time periodic scheduling, the deadline of a periodic thread is conventionally the end of the current period. In contrast, our tests support periodic threads in which the deadline may be earlier than the end of the current period. In the extreme case, the deadline may be specified as identical to the per period execution time, which results in perfectly isochronous periodic threads. The provision of such threads, which we refer to as jitter-constrained threads, helps end-systems to honour jitter as well as throughput-related QoS parameters in distributed multimedia systems. In addition, such threads can reduce end-to-end delay and buffer memory requirements as less buffering is needed to smooth excessive delay jitter.