Would like to do away with my fluorescent lighting in my kitchen and put can lights.

Our problem is we have an upstairs and our joists are running in the wrong direction so we cannot run the wiring in the ceiling to hide it.

Our handyman has suggested running the wires on the ceiling and he would build a soffitt to hide the wires.

I am having trouble picturing this--anyone ever seen something like this or have a better solution?