Not sure exactly what you mean by U shaped.
One point of concern is to determine the direction thet the grain meets the surface being planed. It will always esentially hit the surface at some angle. You want to make sure you feed the board so the angle of the grain is pointing back out of the end of the planer that you are feeding it in from. So the angle is aligned with the direction the blades are hitting the surface (if that makes sense). This would mean one end first for one side and the other end first for the other side (usually).
If the grain has a lot of figure (ie wavy, irregular, changing direction) it may just not work well in a planer. You can try wetting the surface, which will help a little on figured grain.
I haven't worked with Birch too much but I've seen it used in my shop (a lot recently) and they don't seem to be having those problems. One guy mentioned some fuzziness when he edge trimmed some stuff but sharp bits seemed to fix that.