A result obtained by J. Derakhshan and A. Macintyre states that the theory of a mixed characteristic henselian valued field with finite ramification, and whose value group is a Z-group, is model complete in the language of rings if the theory of the residue field is model complete in the language of rings. In this talk, we will see how this result can be generalized to mixed characteristic henselian valued fields with finite ramification, but with different value groups. We will address the case in which the value group is an ordered abelian group with finite spines, and (if time permits) the case in which it is elementarily equivalent to the lexicographic sum of Z with a minimal positive element. In both cases, we give a one-sorted language (expansion of the language of rings) in which the theory of the valued field is model complete if the theory of the residue field is model complete in the language of rings.