  An effective way to reduce clutter in a graph drawing that has (many)
crossings is to group edges that travel in parallel into \emph{bundles}. Each
edge can participate in many such bundles. Any crossing in this bundled graph
occurs between two bundles, i.e., as a \emph{bundled crossing}. We consider the
problem of bundled crossing minimization: A graph is given and the goal is to
find a bundled drawing with at most $k$ bundled crossings. We show that the
problem is NP-hard when we require a simple drawing. Our main result is an FPT
algorithm (in $k$) when we require a simple circular layout. These results make
use of the connection between bundled crossings and graph genus.
