  In this paper, we consider lifts of $\pi$-partial characters with the
property that the irreducible constituents of their restrictions to certain
normal subgroups are also lifts. We will show that such a lift must be induced
from what we call an inductive pair, and every character induced from an
inductive pair is a such a lift. With this condition, we will get a lower bound
on the number of such lifts.
