It should bring it closer. Painting over a white primer will typically take it a shade lighter. Don't be too surprised if it doesn't bring it all the way in. I'm not sure about the Bullseye, but alot of primers can be tinted to the topcoat color, hence avoiding the multi-layers to try to get to the desired color.

Thanks Dave. I would have tinted the primer, but these were test colors/quarts and my wife didn't know what shade she wanted until the last one. Cost me $45 to find out she liked the "last" color. I should have known that.

VVVVVVVVVVVVVery fimiliar with that journey!!!! Alot of paint companies are coming out with little testers for just this purpose. It will save you a ton of money(and frustrations). In my line of work, friends, relatives,etc. tend to head to my house to get my opinion; as if it matters.
Oh, by the way, it's almost always the first or last color they pick for some reason. If it's the first; they haven't figured it out until AFTER you went through the next thirty seven colors!!!!

Heh heh...yeah that's right. We finished the 2 rooms we were doing though, so I only have 4 QUARTS left over...not too bad, huh? I'll find somewhere to slop it on if it's only in my shed.