You're using set angle edges then Tom .. I'm guessing that's by using a sharpening jig ? I sharpen by eye and hand with diamond hones and then strop to produce an even convex edge that flows from cutting edge to main grind bevel. If I am looking for an edge that's solely for silly stuff like Rizla cutting then I'll make the edge finer and more acute. I can cut Rizlas with any of my working edges, but it's easier with an edge prepared for just such stuff. I have done a Rizla cut with my Gransfor Bruks Axe. That axe makes very light work of sectioning green wood I can tell you !

Half the problem with set angle edges (as I see it) is the corner at the transition from primary to secondary grind angles (main blade bevel to edge angle). It 'catches' at the material being cut if a penatrative cut is needed and make the job harder to do. Look at the shape of a racing yacht hull if you want something that will slide easily through material