Finally getting round to fine tuning my zero.

Accuracy was good at 10yrdsish and I though good at 25 yrds (zero).
However when I got round to regularly putting 10 pellets into the same target, I started to see some trends.
At 10 yrds it was hitting consistently 1cm to the right.
And at 25 yrds it was hitting 1/2 inch low and a 1/2 inch to the left.
Figure approximate.

Obviously this cannot be cured by twiddling the knobs....so another solution has to be found.
But what is the likely cause.

Tonight I tried centering the adjustment knobs to start again.
Then slackened of the scope rail clamps and retightend.
Couple of shots at 10yrds an inch left.

Tried slackening off the scope clamps. Then with the rifle supported on two tripods I adjusted the tripods so the reticul was centred on a spot on the target.
When I rotated the scope back and forth, the reticule traced a smile on the target. see mouth left!
Should this happem, or is this a symptom of my problem?
Do I need to shim something, and do I shim inside the rings or between the mounts and the dovetail?

It is an HW77k with two piece four bolt mounts, (so thats 16 bolts in all!)

I'd love to sort this out, 'cause then I can sort out MY technique, and work on getting my zero moved out to 30 then 35 yrds. (The back fence and OH's reluctance to have me firing from the middle of the lounge, prevents a longer zero )

Thanks in advance for any responses.

Pete