Two other considerations: shims and an adjustable scope base.
It is a good thing to start the scope alignment process by shooting at a huge target, maybe 24 inches square at 25 yards. Then rather than using the knobs, use shims to close the vertical gap between the aim point and bullet impact point. (An acceptable 0.0025 inch shim can be cut from an aluminum coca cola can, two of which which will change the point of impact about 1 and 1/4 inch* at 25 yards.) Shim the bottom of the ring but not the top. Once the scope is shimmed with one or 2 of these it will reduce the need to use the vertical knob. I generally start with 1 shim under the back end of the scope and will use up to 4.
Horizontal movement can be done with the screws on the adjustable base, to move the scope from side to side.
Then once these 2 steps are done and the bullet is impacting where it needs to go at 25 yards the process can be repeated at 100 yards. Once I get it within 3 or 4 inches at 100 yards using shims and the base screws then I take it all apart and put Loctite on the mounting screws and shims, let it sit for a day or so and then check tightness again. I also have no qualms about putting a drop of Loctite on the bottom of the scope in whichever ring isn't shimmed.
All this can be done while breaking in the barrel, which makes it a little less boring. THEN is the time to sight in using the scope knobs.
(If a person doesn't want to do all this or if they need more than 2-4 shims Burris makes adjustable rings with inserts that do the same thing easier, faster and with more stability.)
*edited to reflect what I usually do to raise the aim point.