  In this work we describe a method to reconstruct the braid monodromy of the
preimage of a curve by a Kummer cover. This method is interesting, since it
combines two techniques, namely, the reconstruction of a highly non-generic
braid monodromy with a systematic method to go from a non-generic to a generic
braid monodromy. This "generification" method is independent from Kummer covers
and can be applied in more general circumstances since non generic braid
monodromies appear more naturally and are oftentimes much easier to compute.
Explicit examples are computed using these techniques.
