So often, a hybridizer gives you a piece of wood and asks you
to graft it (when you learn how) hoping to get the plant back in the future if
he/she loses it for whatever reason. If it's a thin piece, this
technique is a lifesaver. Thin rootstocks are not always
successful. Thicker ones have a much better take rate for
me...almost 100%.
This time, lay the knife along the bark as shown and gently
push all the way in to the "wood". With a gentle twist
each way the bark is lifted from the wood. (Go opposite the
existing node for one graft, or one-quarter each way and make two
slits to insert two.)
Cut the scion with a long flat cut from side-to-side. Back
trim a little ledge on the back side to slide under the bark more
easily. Now trim just a fine whisker down each edge to bare the
cambium sap line to better connect with the flow.
Here is a picture sequence which may help give the idea.