For a complete discrete valuation field K of characteristic 0 with residue field of characteristic p > 0, consider the problem of embedding a given cyclic extension M/K of degree p into a cyclic extension of degree pⁿ for various n. Let c(M/K) be equal to the maximal n for which this embedding problem has a solution. In this paper we consider relations between c(M/K) and c(LM/L), where L/K is a given extension linearly disjoint with M/K. Bibliography: 5 titles.