since you (supposedly?) can't buy the same bullets as used i the white box i suggest you substitue either Hornady or Sierra bullets of the same weight and design (tipped / softpoint / etc...) and see how well they shoot.
accuracy is what ultimately counts with a bullet of proper construction for reliable 'terminal ballistics'. both Hornady and Sierra have done their homework with .22 caliber bullets from everything i can see.
one thing, however: the Hornady bullets are better in their spire point variation (out of .22 caliber centerfires) for harvesting deer than anything i've ever read about the Sierra's. the 55 and 60 gr' spire points are deer killers beyond what you'd ever expect. i've known a landowner use them to great effect while nuisance hunting.......
ss'