Try using tiles or broken pieces of plates that are relatively the same thickness. That way you wouldn't have to worry about precisely trying to wipe the grout off the lower tile without wiping the grout off the edge of the thicker tile. That or you could try smoothing the edges of tiles that are clearly thicker. Rub them on some concrete to dull the edge so even if you can't perfect the grout, it won't cut the bird's feet. For that matter, depending on what size the broken pieces are, you could try rubbing the bottom of thicker tiles on the concrete to "sand" the thickness down some. Might work? Hope this helps, Dana

I saw somewhere, I think DIY, that if all of your pieces of tile or glass aren't the same thickness, just glue two pieces of the thinner tiles together so they will be even with the thicker ones. Hope this helps.