Thanks for all the responses guys!! I'm sorry It has taken me so long to get back. I'm looking for this information to lap my main tuning slide
to be glass smooth.
I have actually converted an old LA Ambassador cornet (Cheap $30 eBay project horn.) to have a reversed tuning slide with an adjustible finger ring attached to the bottom tube that enables me to operate the main tuning slide with my left thumb. I use a baseball style grip with my left thumb under my first valve slide. This configuration enables me to tune any note (I can even compensate for a flat fourth line "D".) and is far easier and more comfortable than holding the horn with your fingers positioned to operate the first & third valve slides togeather.