A digraph $D$ with $(\genfrac{}{}{0ex}{}{n+1}{2})$ arcs has an ascending subgraph decomposition (ASD) if there exists a partition of the arc set of $D$ into $n$ sets of size $1,2,3,\dots ,n-1,n$ such that the digraphs $D_1,D_2,\dots ,D_{n-1},D_n$ induced by the $n$ sets of arcs in the partition have the property that for all $i<j$, $D_i$ is isomorphic to a subgraph of $D_j$. We will outline a proof that almost all tournaments of order $6n+4$ have an ASD.