Diagonal movement of the crosshair while adjusting the elevation turret.

The only scopes I've owned so far cost less than $300. I have a West Hunter 4-16x44 on my Avenger and a Hawke 2-7 Vantage on my Prod (I have other scopes on powder burners). I like both the scopes on my PCPs but the Hawke scope jumps on me sometimes. Like I turn it 1 click left and see a 1 inch change in vertical at 33 yards. But it settles down and holds zero well. I think it comes with low end scopes. So far, my West Hunter doesn't do this, however. I have a Primary Arms 4-14 in storage waiting for a gun to arrive and I have not seen it with that scope either. So maybe not all low end scopes do it but some do.

The thing I cannot tolerate in any scope is when it does not hold zero. I had a UTG bug buster 3-9 that did that. I sent it back, it was under warranty, and they took it but haven't returned it or sent me a new one. Guess which brand I won't be buying any more. But based upon other peoples comments, I'm sure UTG makes some good ones too.
 
I have very limited experience with optics. So here it is,

The gun in question is an HW35e which has a very noticeable barrel droop. With the optically centered scope I'm getting about 5 inches low and 1.5 inches to the left. So as I adjust the elevation turret up, the poi simultaneously moves to the right, getting the poi closer to the point of aim with each shot. Therefore instead of moving straight up, the poi moves diagonally, if this makes sense.

This has happen to me twice with two different budget scopes ($150-$190) from different manufacturers but the same gun. Someone here suggested that this might be due to a tilted scope. Understandable, but the gun and scopes have been bubble leveled during the setup. I talked to one of the scope's manufacturers just to learn more about this and he told me that if there is too much vertical adjustment going on I could see this behavior. I think he said that this is due to the erector tube not having enough pressure form the internal springs. Whats your take?

Anyhow, I'm using an adjustable mount for this gun which serves me well but brings me another issue, eye alignment. With the adjustable mount sitting too high and the low vintage cheek piece of the gun the eye alignment is off. I'm thinking maybe a cheek riser could be a solution.

I've experienced this a few times over the last 30 years. There are two possibilities.

1) If you adjust either windage or elevation to one of the extremes, your other adjustment (let's say elevation in this case) is bearing on the curvature of the erector tube, causing a windage shift as you adjust elevation.

2) The other possibility (several other replies have alluded to this) is that your scope is not mounted parallel to the barrel's bore. This is the most likely scenario, especially with a break-barrel. One way to correct this is to purchase mounts that are adjustable for both windage and elevation, allowing you to adjust the scope to be parallel with the bore.
 
I have very limited experience with optics. So here it is,

The gun in question is an HW35e which has a very noticeable barrel droop. With the optically centered scope I'm getting about 5 inches low and 1.5 inches to the left. So as I adjust the elevation turret up, the poi simultaneously moves to the right, getting the poi closer to the point of aim with each shot. Therefore instead of moving straight up, the poi moves diagonally, if this makes sense.

This has happen to me twice with two different budget scopes ($150-$190) from different manufacturers but the same gun. Someone here suggested that this might be due to a tilted scope. Understandable, but the gun and scopes have been bubble leveled during the setup. I talked to one of the scope's manufacturers just to learn more about this and he told me that if there is too much vertical adjustment going on I could see this behavior. I think he said that this is due to the erector tube not having enough pressure form the internal springs. Whats your take?

Anyhow, I'm using an adjustable mount for this gun which serves me well but brings me another issue, eye alignment. With the adjustable mount sitting too high and the low vintage cheek piece of the gun the eye alignment is off. I'm thinking maybe a cheek riser could be a solution.

I've experienced this a few times over the last 30 years. There are two possibilities.

1) If you adjust either windage or elevation to one of the extremes, your other adjustment (let's say elevation in this case) is bearing on the curvature of the erector tube, causing a windage shift as you adjust elevation.

2) The other possibility (several other replies have alluded to this) is that your scope is not mounted parallel to the barrel's bore. This is the most likely scenario, especially with a break-barrel. One way to correct this is to purchase mounts that are adjustable for both windage and elevation, allowing you to adjust the scope to be parallel with the bore.

There IS one more possibility-maybe the tracking system isn't aligned with the reticle. 
 
I have very limited experience with optics. So here it is,

The gun in question is an HW35e which has a very noticeable barrel droop. With the optically centered scope I'm getting about 5 inches low and 1.5 inches to the left. So as I adjust the elevation turret up, the poi simultaneously moves to the right, getting the poi closer to the point of aim with each shot. Therefore instead of moving straight up, the poi moves diagonally, if this makes sense.

This has happen to me twice with two different budget scopes ($150-$190) from different manufacturers but the same gun. Someone here suggested that this might be due to a tilted scope. Understandable, but the gun and scopes have been bubble leveled during the setup. I talked to one of the scope's manufacturers just to learn more about this and he told me that if there is too much vertical adjustment going on I could see this behavior. I think he said that this is due to the erector tube not having enough pressure form the internal springs. Whats your take?

Anyhow, I'm using an adjustable mount for this gun which serves me well but brings me another issue, eye alignment. With the adjustable mount sitting too high and the low vintage cheek piece of the gun the eye alignment is off. I'm thinking maybe a cheek riser could be a solution.

I've experienced this a few times over the last 30 years. There are two possibilities.

1) If you adjust either windage or elevation to one of the extremes, your other adjustment (let's say elevation in this case) is bearing on the curvature of the erector tube, causing a windage shift as you adjust elevation.

2) The other possibility (several other replies have alluded to this) is that your scope is not mounted parallel to the barrel's bore. This is the most likely scenario, especially with a break-barrel. One way to correct this is to purchase mounts that are adjustable for both windage and elevation, allowing you to adjust the scope to be parallel with the bore.

There IS one more possibility-maybe the tracking system isn't aligned with the reticle.

Very true. If bubble-leveled, this can be pronounced. Rarely are the turrets vertically/horizontally aligned with the reticle stadia on cheaper scopes. But being a break-barrel, the odds of the barrel being misaligned with the scope tube is the greatest probability. A windage & elevation adjustable mount can fix this.