Recently the paradigm of skew-tolerant parallel asynchronous communication was introduced, along with constructions for codes that can tolerate or detect skew. Some of these constructions were improved in [SI. In this paper these constructions are improved upon hrther, and we prove that the new constructions are, in a certain sense, optimal. Index rem-Parallel asynchronous communication, skew, error correcting codes, unidirectional errors, t-error correcting/all unidirectional error detecting (EC/AUED) codes, pipelined transmission.