  A drawing of a graph is fan-planar if the edges intersecting a common edge
$a$ share a vertex $A$ on the same side of $a$. More precisely, orienting $e$
arbitrarily and the other edges towards $A$ results in a consistent orientation
of the crossings. So far, fan-planar drawings have only been considered in the
context of simple drawings, where any two edges share at most one point,
including endpoints. We show that every non-simple fan-planar drawing can be
redrawn as a simple fan-planar drawing of the same graph while not introducing
additional crossings. Combined with previous results on fan-planar drawings,
this yields that $n$-vertex-graphs having such a drawing can have at most
$6.5n$ edges and that the recognition of such graphs is NP-hard. We thereby
answer an open problem posed by Kaufmann and Ueckerdt in 2014.

Computational Geometry