One way to deal with this is to tie an overhand knot in your tippet - but leave it open. Place your split shot inside the knot with the cross over in the split shot opening. Tighten the knot and then close the split shot.
Because the knot hasn't closed on itself, it will not weaken the tippet. The shot will not fall off nor will it slide down the tippet.
I generally use Dinsmore but also Gremlin Green.
-Steven (from Hyde Park)
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