Jumping and drifting

Today's lesson started with some flat work, and then we switched to jumping, after John scolded me for not wearing my shirt tucked in with a belt.  Actually, before the lesson even started, Katy helped me adjust Duke in a different bridle, which included punching new holes for his tiny head.
Duke seemed much more pliant in the tighter noseband and flash, but I couldn't tell if it was the ride yesterday, the week with John, the tighter noseband, or a combination of all of the above.
John had us work again on bending him both ways, including the awkward actual use of the bicep to pull his head around, but it was easier today to remember to also push forward with the outside hand.
We started by trotting over a little cross rail, and John said to focus on the trot - don't think about the take off spot, but just think about the rhythm of the trot and keeping it all the way to the fence.  No big deal.
Then we did some canter, which was ok, but Duke was preferentially landing on the right lead even though we were going left, and then John did something miraculous and said to listen to him, and then as we took off, told me to use my right leg (?) and Duke landed on the left lead perfectly.  His timing was impeccable and it was a huge eye opener that I'm not using that leg aid enough, just kind of hoping he'll magically guess which way I want to go.  However, it's a bit disappointing that a few hours later, I don't remember which freaking leg it was during a jump in the air to ask for the lead.
Then John switched us to a vertical, but at an angle, first coming at it angled to the left, then after a few times, from the right.  Duke found it much more challenging to angle it from the right, and would take off with his running thing.  John said it was good, because we found the hole, and so we'll know that he doesn't want to use his right inside hind and would rather run than balance.  He had me once halt and rein back, but mostly just fix the lead and then make a circle.
What worked the best was one good pull - almost a pulley rein - and then immediately release with both hands, and Duke would soften back up almost immediately.  If I just got in a pulling war with him, he just tore around with his head down.
From there we did the 4 stride line from the vertical which we'd been angling to an oxer, which he did very well, and then a bending 5 stride line from the Seahawks vertical to the same vertical.  Then we finished on a brown gate, which he jumped perfectly, and John said "Walk!"
John said in show jumping, I'll have to use my hands more than he'd like, but try to get him one good sharp pull and rebalance him.  Make sure to balance him 5-6 strides out, and don't get into a pulling war with him during the course - give the correction and then release.  A few times he had me bend him before the fence, but it was really hard to bend him while keeping the line to the fence.
He jumped a few short and a few long, but he's easy to stay balanced over, even if I don't like the take off spot.
So I think it is going to be talk low to him (whoa, easy, steady; in a low voice), think way out to steady him (half halt, sit up, think rhythm), balance him, and bend him, and then give sharp corrections if we barrel through any fences.  He was, all in all, much better.
It was pretty hot out today (low 90s?) and even his eyelids were frothy with sweat.