Ken, from what I’ve seen perusing as many pics as I could find, it seems that nearly all of them have the “straight” side against the rest of the piece, with the “slanted” side facing outward towards the end of the tenon.

Gustav Stickley also shows them with the flat side in and the slanted side out in several of his designs in a book of 62 craftsman furniture plans…they are shown this way in the plans/diagrams for several designs in this book.

Paul or one of the others may have something else to say on the matter, but from what I can tell, this seems to be fairly standard.

I think this begs another question, however. Does the mortise itself need to be slanted on one end as well? It would seem to me that this would be the case, but perhaps not.

It depends on the scale and application. As the joint increases in size then it becomes much more important to have the orientation of the wedge as stated above. If the wedge is being used in an application similar to my first drawing then it always matters. The wedge is used to apply force perpendicular to the direction in which is inserted. In order to stay inserted the wedge relies on friction. To have this friction, you need to mate the surfaces of the wedge as closely as possible to the mortice in which you are inserting it. In small wedged tenons, like Ken asked about, the wedge is generally inserted into a saw kerf. As the joint increases in size you need to actually saw out a wedge area in which to insert the wedge. Thus making the orientation and/or shape of the wedge very important.

Wedges have the straight side against the tenon and the angled edge to edge of mortise. As you normally make mortise slightly wider the side you nock wedges in.
If putting wedge in from each end of tenon down a saw kerf keep angle facing the edge of mortise in fact the same way as above as the angle of the wedges above this pushes tenon out to edge of mortise.

Also remember to tap one wedge then tap the other wedge until you have got enough of both wedges down to make a good fixing. DO NOT drive one wedge all the way in then the other.

You can also put wedges in a blind mortise and tenon joint. Make mortise slightly angled so wider at the bottom. Then putting saw kerf from each side of tenon. Do not make wedges too long as could split timber. Insert wedges into saw kerf and assemble joint. As end of wedges hit bottom of mortise the wedges spread the tenon almost giving a dovetail effect. This is normally a one shot operation once assembled would be very difficult to get apart. This joint known as fox wedged mortise and tenon.

Tusk tenons like what Greg showed firstly. I was taught to do that in a similarly way that you would draw bore pin. In that you would offset mortise by say 1/16th” through the extended bit off the tenon.

I did learn some stuff at college