A digraph $D$ with ${n+1} \choose {2}$ 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.