Last year I finished what our Japanese Landscape Designer calls a "Yamaga" or Mountain House style roofed gate. He pointed out that my joint wedges were incorrect and should be replaced. My wedges were placed with their angled surfaces on each other so the flat surfaces fully engaged the upper surface of the joint above, and top of the beam on the lower wedge bottom surface.
He instructed that each wedge angled surface should engage the top - outside corner of the joint, and the wedge flat surface should be flat against the beam. What is the correct traditional Japanese method for wedging?

A picture is worth...

The Japanese employ, in temple architecture, both configurations of opposed wedges in construction that you described above, and there is also use of a single through-wedge instead of an opposed pair of wedges. I would need to see the particular application for this joint to comment further.

~Chris