I studied with L. Frink at NYU and so I have it from the horse's horse's mouth, so to speak. I was a 6+ year buzzing basics guy before studying with Laurie. I still did and do buzzing basics 1-4 every day, but her system really helped be break through some barriers and gain much more control and physical awareness on the horn as well as helping me to get my C/Eb/D/Pic up to speed with my Bb/Flug. This system is GREAT. I highly recommend getting a lesson with Laurie and/or getting her book: "Flexus". It is very well laid out. I am no longer studying with Laurie as I have graduated and moved to Miami for my DMA. I'm in the process of sorting out the Myriad of exercises (far more than listed below) and reconciling them with what works and what doesn't work for me via practice logs. I'm currently doing more buzzing basics and fewer Caruso things (although still at least one from each flexus category per day). At the time of graduation, I had about 10 separate, and mutli-part, things on my daily practice list that did not include buzzing basics or any practice of any music or improvisation work!
You can and should play as low as you can with any fingerings. Playing the first pedal octave should be done without getting out of position, but after that, the idea is to get the chops relaxed. After pedals, play a steady chromatic scale up and down from low C up to your comfortable range. This is to get the chops used to getting back into focus and to work on the different types of energy needed to go up, switch direction, and come back down. Do pedals after the interval studies, after harmonics, and after particularly strenuous developed scale exercises.
Done with the long setting (nose breaths, don't reset). This is a range builder and a fantastic one because it's via interval, not via buttocks-clenching. Doing it PPP will help aid with being able to play very loud. At first you can't, then you can and it sucks/is wrong/sounds bad, then you can and you work on it.
The preliminary caruso thing. Use the long setting and when the first one is mastered, make it more challenging ala "flexus". Subdivision is crucial as this is coordination training. It's also about being able to move the chops WITHIN the mouthpiece to change registers without taking the mouthpiece off and putting it back on. This does not mean to have ZERO physical movement, just nothing that requires lips to lose grip with the rim. You also don't need to be tense the whole time.
by alternating the naturally more efficient slurring and less efficient tonguing, this promotes a unified set-up for tonguing and slurring. Flexus has more on this under the articulation heading. No long setting here. This one was a real zinger for me and I owe much of my progress to it! I had no idea how out of sync my articulations were with respect to how good I was with the slurring of just about anything.
This is an advanced, long setting exercise that goes through your whole range with a single setting. Flexus has a slightly different approach. I found that I needed lots of chromatic scales to figure out exactly where some of the upper register notes sat on my equipment. In most cases, they sat way lower than where I was trying to put them. I found that I was getting all the way to DHC in harmonics, but on the gig I never could seem to lock it in.
This system acknowledges that moderately learned musicians know how music goes, and that they know what sounds good and what sounds bad. The hypothesis is that when we can't play something well, coordination of the muscles in execution are at fault rather than a faulty musical concept or approach. Hopefully these words will inspire others! I've had numerous students as a GA who I have use this system with (in addition to buzzing basics) and it's all good. But everyone is different so just simply doing everything and moving on is no guarantee for success!