This document discusses universal lossless source coding for independent piecewise identically distributed (i.p.i.d.) sources. It proves that Bayes codes, which are universal source codes, minimize the mean redundancy asymptotically for i.p.i.d. sources where the number of stationary segments increases to infinity as the data size increases. Specifically, it shows that the mean redundancy of the Bayes codes does not depend on the coding probability and equals the Bayes redundancy asymptotically, demonstrating that the Bayes codes optimize compression in this scenario.