  In 2009, Bang-Jensen asked whether there exists a function $g(k)$ such that
every strongly $k$-connected $n$-vertex tournament contains a strongly
$k$-connected spanning subgraph with at most $kn + g(k)$ arcs. In this paper,
we answer the question by showing that every strongly $k$-connected $n$-vertex
tournament contains a strongly $k$-connected spanning subgraph with at most $kn
+ 750k^2\log(k+1)$ arcs.
