Best way to remove a saddle valve?

I want to completely remove a leaky saddle valve which once fed an icemaker water line ( no longer in use). What's the best/easiest way to permanently remove the valve and seal the remaining hole in the copper pipe? I prefer NOT to cut the line and solder in a coupling.
Mike Wake Forest, NC
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From the MacGuyver school of plumbing:
The saddle valve I used left a very small hole. I've done this by removing the clamp, placing a big enough, square piece of rubber (bike inner tube) over the hole and holding it in place with a thick hose clamp. Unorthodox, sure. Against code, you bet. But cheap, very easy, and still working without a drop after 10 years. Mine is in a place where I can keep half an eye on it and if it does eventually fail it won't do much damage. I also theorize that if it does fail it will drip first, not a catastrophic failure.
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Best way: Shut water off, drain line, cut past hole, cap,and sweat.
Barring that...cut off water...open a valve near the location where the saddle tap was, using an air compressorblow the water OUT of the line, and sweat a bit of solder into the hole..
Its much easier to cut the line and fix it right.

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Permanent requires the cut and sweat. A long term semi-permanent repair can be made with a clamp repair kit available for a few $ at plumbing supply houses. It is a clam shell like device with heavy rubber pads that wrap around the pipe and secure with bolts. To code and legal in most places in exposed locations.
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Mike Wood wrote:

wont take long, but will last long time.. cut the copper pipe and clean up the joint area and the joint... pull the pipe apart and put in the joint with flux on it. then heat it up and put the solder to one side of the fitting and then the next.....dont try to patch up the small hole.. the company that built my house repaired a nail hole in the copper pipe for the kitchen sink... a few years after moving in we could fell the floor (concrete floor) kinda hot right infront of the sink... traced the problem behind the sheetrock under the kitchen cabinet.... the tiny nail hole that was soldered finally leaked....just cut out a piece of copper tubing and replaced that whole secton of 2 feet....
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