  Hurwitz numbers count ramified genus $g$, degree $d$ coverings of the
projective line with with fixed branch locus and fixed ramification data.
Double Hurwitz numbers count such covers, where we fix two special profiles
over $0$ and $\infty$ and only simple ramification else. These objects feature
insteresting structural behaviour and connections to geometry. In this paper,
we introduce the notion of pruned double Hurwitz numbers, generalizing the
notion of pruned simple Hurwitz numbers in \cite{DN13}. We show that pruned
double Hurwitz numbers, similar to usual double Hurwitz numbers, satisfy a
cut-and-join recursion and are piecewise polynomial with respect to the entries
of the two special ramification profiles. Furthermore double Hurwitz numbers
can be computed from pruned double Hurwitz numbers. To sum up, it can be said
that pruned double Hurwitz numbers count a relevant subset of covers, leading
to considerably smaller numbers and computations, but still featuring the
important properties we can observe for double Hurwitz numbers.
