The "Stevens palming exercise" was an exercise to help you reduce playing pressure.

Mendez played open arpeggios up to and above high C on a horn that was suspended on a string hanging from the ceiling.

I've seen people lay horns on tables or on a shelf to play open arpeggios.

Stevens had the student lay the horn on their open palm. They held the bell up about 10 or 15 degrees higher than parallel to the ground. Then they set for the upper register and played open arpeggios up and down. With no pressure.

I have people touch thumb to thumb on the mouthpiece side of the valve casing. And touch middle finger to middle finger on the bell side of the valve casing. They support the bell and leadpipe this way. Allow the horn to slide toward and away from your mouth. If you use pressure the valve casing will touch the middle fingers. You then place the horn back in the middle and try less pressure. I feel safer letting students do this with a good pro horn. There is less chance of dropping it AND it helps to break the death grip that so many players use on the valve casing. I also have them hold the bell up about 10 or 15 degrees higher than parallel to the ground. Then they set for the upper register and play open arpeggios up and down. After a while they play valveless songs (above high C). Also with no pressure.

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Best wishes
Clint 'Pops' McLaughlin