Just found that term, and it still makes me giggle, but describes my horse's back perfectly.
He's a TB, normal to high wither (but not like a sharkfin), but has a spine that makes the channels too close to his back. He's not skinny at all, and while his topline could use more muscling, it's a slow go and a lot of it is conformation.
He'll fit into any dressage saddle I have (all Med Narrow and Mediums) because of the higher pommel, but close contact saddles have been a pain.
Bonus points if it's a long or forward flap- I'm 5'11 all leg.