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I use anhydrous lanolin on my instruments and that stuff is SUPER THICK. Look into getting some, from a pharmacy. Add valve oil (or lamp oil) to adjust consistency.

Another option is to tie a shoestring or something onto it to keep it from slipping. Definitely not a perfect solution.

If that doesn't work, try this:

Take your horn in to a good repair person. They can tweek the slide tubes a bit and cure the problem. I wouldn't do this at home. It should be a fairly cheap repair. No matter what oil or grease I tried my slide would still slide a bit when I didn't want it to.
Good luck, Phil

A few years ago, the Maytag Corporation decided to streamline its catalog and only offer basic models of its washers and dryers. The payroll was also cut down. Quality suffered. The once lonely Maytag repairman now had so much to do, he couldn't fix all the machines.

What this has to do with the problem of the loose slide is, what if all the tubas (of this brand) have a loose tuning slide?

Just wondering.

What brand and model of tuba is this? Miraphone 1291s have that problem a lot. Just use the thickest slide grease you can find and reapply often.