| You didn't say "how short" in terms of how many wraps you can get around the post with the short string. The issue you describe with the nut is because the break angle of your string over the nut is not sufficient. I suspect what you have is perhaps one or one and a half wraps on the post? Most times A strings don't have a string T to increase the break angle over the nut. If you have a long enough string to make many wraps around the post, the upper winds should press the string down low on the post, making the break angle good. Why don't you try this- insert the string into the center hole of the post, and make a wrap, then see if there is enough left to go OVER that wrap like an X which will cause the first wrap to be held under the second wrap. If you don't have enough string for that, you could jury-rig up a splice but that is pretty iffy and you'd likely get major tuning issues. Best solution is to buy a new string. I usually only trim my E string. I get about 4 wraps on the E, A and D, and 3 wraps on the G.
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Luckydog
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So I just restrung and low and behold I cut my A string a tiny bit to short, and I mean a tiny bit. It's not fully descending into the groove in the nut and when I switch from a higher string (D or G) if i push up on the A string it pushes it out of the groove, new a string already? 
