  We investigate the model completeness of the theory of a mixed characteristic
henselian valued field with finite ramification relative to the residue field
and value group. We address the case in which the valued field has a value
group with finite spines, and the case in which the value group is elementarily
equivalent to the infinite lexicographic sum of $\mathbb{Z}$ with a minimal
positive element. In both cases, we find a one-sorted language 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.
