The most important thing to get your horse to be drawn tight is to have impulsion, he needs it to rise his back and give in to the reins (so you have to keep the same tension on the reins so that he can fix himself).
Do a lot of transitions to make reactive to your applications.
You need to watch at your exterior rein to keep the straightness of his body.
You can also try to work him on counter-bending so that he will be straighter.
I hope i could help you, good luck :)