Most lip flexibility books start patterns with open-finger combination notes and then go to the lower fingerings (some exceptions are the Irons, 27 Groups of Exercises, and some of Scott Belck’s exercises). Open fingering usually feels easier to students because of the relatively short length of tubing. But in my experience, most students have great difficulties with the lowest valve combinations (1-2-3 and 1-3).

By starting lip flexibility exercises with the lowest combination, and working up from that, students start out trying to conquer the relatively-stuffy 1-2-3 combination, and they stick with this difficulty until they can do it better. Then they get to move on to higher (and easier) tubing lengths. It’s like eating your greens first, and then getting your dessert. I don’t recommend doing this all the time, but I do recommend trying this low-to-high sequence often.

In addition, try pulling out on the third-valve slide for the slur exercises on 1-2-3 and 1-3. This will be more in tune and give you a better expectation of the way these alternate fingerings should be played if you have to use them in the upper register.