By the way, my post wasn't snarky...just curious from an environmental standpoint. I always assumed that the dual use was better since it's only one offense.
Yeah, sorry. The answer is it depends.
If your newspaper is delivered in an
enviromentally friendly bag, by all means use it twice and let it bio-degrade in the landfill with your pet waste.
If your newspaper is delivered in a recyclable bag (for example, in SF a #2 plastic), you're better off recycling it with your blue can recycling (not using it twice if that means that it won't go in the recycling bin, but if it means using it to keep your recyclables, then use it twice). There should be a number on the bottom of the bag to let you know, then check with your waste company to see what # plastics they recycle.
If your newspaper is not delivered in a recyclable bag or enviromentally friendly bag - write an op-ed to that newspaper encouraging them to get with the program. It's 2010 for god's sake!