Jumping the 4 stride line

We had a quick jump lesson tonight.  John started us over the cross rail, and, for some reason, Duke just kept nailing the distance, whether we were coming from the right or left (and nailing his lead when I asked him to change in the air over the fence).  So John made it a vertical, then an oxer.  Duke, bless his sweet heart, just kept jumping it exactly right.
So then we did the four stride line coming off the right lead, and the first couple times in he had a hard drift left, but then I did a better job lining him up further out and then keeping my left leg and hand on him, but interestingly, we had to really push to get the fourth stride.  Then we did it off of the left lead, and the last time through, I thought we were going to miss the distance, so I gave him a nudge a stride before the first fence, and man, that really helped him cover the four strides (instead of waiting to nudge him until after we landed after the first fence).
John said he really likes that Duke will try his best, no matter what we put in front of him, but that we'll need to keep in mind for shows that if it is a bit of a long distance, and I ride him straight all the way through, he's going to compress a bit when he is going straight, so I'm going to have to push him a little bit harder all the way through.
He said something else brilliant too, but now for the life of me, I can't remember it.
Over the last few days, we seem to have moved past the bit obstacle.  I used little bits of carrots and one day one of his favorite peppermints, as well as putting his bridle on in his stall when we're at home.