Refinement of a technique - detached scion grafting. This was the first grafting technique discussed in this thread in which a scion cut from the same or different tree. In the pictures and videos I showed on the subject, the wedge was made with one cut on the understock. When grafting to a branch on the understock that is much larger than the scion, try three parallel cuts instead like in this picture from Boon:
It will reduce pressure on the scion and reduce the tendency for the scion to be pushed out of the cut.