We prove coding theorems for list codes for compound channels and for codes within codes. The theorems imply corresponding results for what are usually called simply “codes”, which are list codes where one is the maximum decoding list length permitted to the decoder. The Bergmans coding theorem for degraded channels ([4], Theorem 15.2.1) and the positive part of the Wyner-Ziv theorem ([4], Theorem 13.2.1) are easy consequences of our results.