in my relatively limited experience, related to alot of the other members of this board, i have found that convexed knives get very sharp (i recently shaved my face with on that i made from an old paring knife that i fully convexed).
i convex the knife by laying it down flat on a sheet of sandpaper, starting with 200 grit if i am totall reprofiling it, about 400 if it is dull, and about 600 if it just needs some touching up. some people go into the thousands, but i find it unneccesary. i lay the sandpaper down on a peice of cardboard (you can use leather) and hold it at the edge with my fingers. i lat the knife down flat on the sandpaper, and drag the knife edge trailing along the length of the paper, pushing down hard. i do this several times on each side until i have a nice even finish on both sides and the bevels slope smoothly to the edge.
i then repeat this process with progressively finer grits of paper until i have a nice satin finish on the blade and the edge is pretty sharp. it will often have a small burr on the edge still. i then very very lightly (not pushing, only letting the weight of the knife push down) drag the knife along the surface of a fine bench stone at about three times the edge angle (normally about 40* or 50*) with the edge leading a couple of times. this will get rid of the burr and leave you with a sharp knife. i then strop on an unloaded leather belt, rough side and then smooth side. i have read that you can get better results using compound on a belt, but i don't have compound yet.
did i mention that i shaved with a knife prepared this way? you can get really good results doing this.
before i got sandpaper and cardboard, i used a cheap benchstone from the local hardware store. i think it cost five dollars and change. i would pull the knife towards me, edge trailing, first with it laying flat and as i pulled towards me i would slowly life the spine of the knife along the length. this would round out the shoulders of the bevel and fully convex the blade. i prefer the sandpaper though because it gives a more consistent finish to the edge and it is a little bit easier for me.
also, the fully convexed edge will in most cases be a better cutter than a knife with anything less than a fully ground bevel, all the way to the spine. as with a scandi grind, the shoulders of the bevel will create friction between the knife and whatever you are cutting. a convexed edge, even if it is not fully ground to the spine, will not have shoulders. it will smooth out the transition between the flat of the blade and the bevels, reducing friction and allowing for a more efficient cut.
