Boolean Union troubles

 From:  Jacob
3930.3 In reply to 3930.1 
Another question about the above model:

Is there a method to "split" a surface without dicing up the solid? I would like to split the tablet's upper surface into "bezel" and "screen" areas to make it a bit easier to work with in modo but I'd rather keep it smooth, rather than beveled/extruded/inset/grooved/whatever.

Thank you!