Bart, I started doing splice grafts Alan's way: cut both the stock and the scion with the clippers, stick 'em together, and wrap. (The precut tape is already hanging on the stock, waiting and ready.)
On clefts I use a knife, laboriously and gracelessly whittling away at my poor scion in an attempt to convince it that I am its master. Sometimes it works. Well, mostly, in fact, but I do have trouble getting everything just as I think it should be. With pear and apple and the occasional plum I get away with it. Apricot not so- but I'll blame the temperature as much as my technique for that. Here it can be difficult to get enough days that are warm enough for the apricots to callous reliably. I've only ever succeeded with apricot using a chip graft.