  We continue the work of Kaplansky on immediate valued field extensions and
determine special properties of elements in such extensions. In particular, we
are interested in the question when an immediate valued function field of
transcendence degree 1 is henselian rational (i.e., generated, modulo
henselization, by one element). If so, then wild ramification can be eliminated
in this valued function field. The results presented in this paper are crucial
for the first author's proof of henselian rationality over tame fields, which
in turn is used in his work on local uniformization.
