Head bobbing method

Hmm, I’ve always been able to detect a similar amount of movement in both axes when using a non-AO scope. Sorry, what you are describing sounds very unusual. 

BTW, if you tend to do a lot of your shooting at distances from, say, 20-40 yards...you may want to adjust your objective lens to give good focus at around 30 yards. Most non-AO scopes are set at 100 yards at the factory so they are hopelessly blurry and prone to parallax error at typical airgun distances. 
 
I'll be the bad guy.... Don't care....

I focus on the same check weld and thus eye position for each shot (so always the same). It's taken a long time (especially across changing rifles) but when I am motivated to 'bob' high/low or left/right that movement actually messes me up. Repeatable position = If I miss because of aim - I screwed up because I cant sit still/steady enough! I do blame one on a bad pellet when I can get away with it. But I'll never profess to be 'good'.
 
Jcd uses the method we should all strive for. The repeatable hold position. Unfortunately it takes a ton of practice (think tins of pellets to perfect). With parallex should be noticeable in both up and down and side to side. If its not then very possible your not dialed in perfect. Some people brains can compensate for one direction or the other. I have noticed that as I get close to dead on i dont notice up and down shifts but I do notice side to side.
 
Yes, head bobbing is important to determine if parallax is spot on. Many people assume if the image is sharp, the parallax is correct... and they are largely correct, but not specifically correct. I went to the range, which had range markers to calibrate the snail on my Bulldog scope. The hard part about horizonal headbobs is the fact you end up bumping the stock and shifting the view due to the stock being moved more than the bob actually moves it. This is why I tend to use vertical bobs for parallax checks. Horizontal bobs can cause shifts which have nothing to do with an actual parallax error.

1534904556_10501164385b7cc8ecf34069.76365272_Scope Snail zoom.jpg

 
I adjust me "fast focus eye piece" till the reticle is sharp AND the reticle stays "welded" to the aim point when I move my head and eye from side to side. The reason I do this is to minimize aiming error at the close field target killzones that are small (about 3/8" to 1/2" diameter) if my eye placement isn't perfect. As long as a shooter has the ability to place his eye in the exact same position in the ocular I really don't think a perfect eyepiece setting is critical, however I'm not that consistent that I can ignore a "wandering reticle with eye placement".

I first learned about the "head bop" method from the field target duo known as the "A Team" and I've been using this method ever since. I can no longer find the direct link to the "A-TEAM-RAY" web site but I did find a PDF of "The "A" Team’s method of Parallax Adjustment and Scope Preparation"..........

http://www.bcsportsmen.org/ft/A_Team_Parallax_adjustment_procedure.pdf

Anywhoo.......I do my setup upstairs at 18 yards and as long as the reticle doesn't move more than about 1/2 pellet width (.177 cal) when I move my eye from extreme left to extreme right I consider the adjustment "good enough", then I put a wrap of black vinyl electrical tape around the fast focus eye piece to keep it in position.............


 
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Redcrow I have a Hawke Air max 30 sf 4-16


Hmmm. I have an Aeon 10-40X56 that is a PIA because sharpest focus and zero parallax and definitely NOT the same. With that scope, if you eliminate parallax using whatever method, you will have a somewhat fuzzy image. I also have a Hawke Sidewinder that does not exhibit this behavior. I suspect your Airmax behaves more like my Sidewinder that the Aeon.