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From what I remember, Honda specifically warns against "friction modifiers" such as STP, Duralube and Slick 50. Those additives might be "compatible" with other oils.... but they still disturb the chemistry of existing oil in unknown ways. And when it comes to my engine, I don't like "unknown".
For most drivers a simple inexpensive synthetic like Mobile 1 ($4.50/qt during Costco sales) is more than sufficient if changed often enough. In fact, even regular oil is soooo much better than it used to be.... that's why you see the service descriptions like SE, SF, SJ.... going up all the time. That's also why Consumer Reports found no difference in their big taxi cab study. But especially hard drivers -- that would be US! -- or those seeking extended drain intervals should consider upgrading to a superior PAO or ester-based synthetic like Amsoil if it's within their budget. Often the extended drain interval will itself compensate for the additional expense. As a case in point, Amsoil's Signature Series 2000 (now discontinued) used to offer a 35,000 mile/1 year warranty. No that's not a typo. And oil analysis backed it up. That particular oil had a very expensive ester base (not the cheaper PAO) that also gave considerably better gas mileage, averaging 7%. With high RPM engines even more. I ran an Integra mostly at 3000rpm and got +3mpg versus regular oil, about a 10% gain.
By the way, better MPG happens in two ways. First because most synthetic oils reduce friction between moving metal parts, right? That's generally a given. But better gas mileage can also happen because of a reduction in the oil's "internal fluid friction" (Geek Note, see the Reynolds Equation:
http://en.wikipedia.org/wiki/Reynolds-averaged_Navier–Stokes_equations) which is a significant factor in engines that consistently operate over 3000RPM.... or, ahem... in Vtech mode. Sadly, instead of using high quality, expensive esters Amsoil is beginning to use the cheaper method of adding extreme pressure agents. That way they can maintain dominance in the Four Ball Wear tests (ASTM D-4172) when compared to other oils. Unfortunately, and here's the kicker.... extreme pressure agents cause premature degradation of the oil. Amsoil knows this fact quite well.. in fact, they drilled it into me during their intensive training for industrial dealers years ago. (Yes, now I know just enough to be dangerous!) Still, be careful with these new Amsoil lubricants that have extreme pressure agents. I doubt they represent the same Amsoil that has become so respected over the last 4 decades.
More on this later in an AMSOIL/Synethic Oil thread.