If a board, counter top or tabletop won't stay flat and wants to cup, and I need it flat on its own merit, I'll kerf the board lengthwise on my tablesaw with the grain, on the bottom or backside, push/clamp it down flat, and glue in a strip of matching wood. I've attached a photo-essay of the process. While I show the kerf running all the way out the end of the wood for illustration purposes, on pieces that the end-grain will show, I stop short of the end so that you can not see the glued in strip(s).
I use this technique to flatten both lumber and plywood. If I'm flattening plywood, like for a counter top, I won't go through the hassle of glueing in a wedged spline, 'cuz you'll never see it. The technique is the same technique as kerf-bending, but the objective and results are just opposite (curved to flat instead of flat to curved).
I'll make the splines rectangular, the same width as the fattest part of the wedge, and then either block plane or sand the spline to fit. It can be full length or pieced in.
Depending on the piece and the amount of cup, I will choose a depth of cut for the kerf. For a large solid wood tabletop, I will kerf only as far as I feel I need to to get the cup out. On utility items, I generally kerf deeper for speed's sake.
(Drawings done in Sketchup!)
(How many people wanna put odds on this technique showing up in a woodworking rag within the next 2 months? )