It looks like you've removed the image from your last post. I saw it earlier and it was much better in my opinion. The gradation from left to right was there but it wasn't too bad and there wasn't nearly as much flare coming back to the dogs head. That was evident from the greater contrast between the peak of the head and the white background, which was significantly different and much better than in the first image you posted.
I don't meter backgrounds the way most people seem to do it. I was taught and continue to meter my backgrounds using reflective spot metering rather than incident metering. I realize that Lastolite recommends 2 stops above taking aperture but that's not very scientific. It's more of a generic number that will ensure that the whole background is white but should not be taken as a definitive number to be used every time you want to turn a background white.
I take reflective readings because there is a constant that isn't there with incident readings. For instance, if I have a gray background and I have a white background and I want to render them both as pure white using incident values then the number will be different for each of them because you're metering the light that falls on the background and you'll need a different amount of light to render gray as white than you will if you were rendering white as pure white.
By taking a reflective reading you don't have this problem. It will still take a different amount of light but you're not concerned with the light that falls on the background. You can meter any color or type of background and as long as you meter 4 stops reflective over the incident subject exposure you'll always render pure white, whether you have a black, gray or white background.
An example of how the 2 stop recommendation doesn't hold up is in my own studio with white seamless paper. I use Savage Super White seamless and when I setup for a 4 stop reflective difference to achieve pure white and then take an incident reading at the background I show 1.5 stops difference between the subject area and background. If my background was gray I'd have to arrive at a new number for the incident value but my reflective reading will still be 4 stops over the incident subject exposure.
So if I meter f/8 at my subject then I know I need to see f/32 reflective from the background. If I meter my subject at f/4 I need f/16 reflective from my background. As long as I have a 4 stop difference I'm in business.
If you were using incident readings you would have to guess, chimp, check it on the computer or go overboard and blow out the background to ensure pure white, which is what most people do, and it's a bad practice.