"Backwoodsman, as you say harm to the guitar isn't an issue. It always seems to me that changing one at a time calls for less retuning before they stay tuned. Certainly this could be my imagination or some other thing I might do alter in my method causing the difference, but it sure does seem that way."

I take them all off, put the new ones on , tune them once, stretch them by pulling up at the 12th fret a few times, tune them again. They stay in tune from there on. Whole job takes max. 20 minutes.

One of the other causes of tuning instability on new strings, especially on modern guitars which have slotted pins instead of solid pins and slotted pin-holes, is the ball-ends not being pulled up tight to the bridge-plate. The initial stretching which I mentined above helps to ensure that the ball-ends are firmly in contact with the bridge-plate.