Firstly I allowed a sucker to grow from the bottom of the Privet (this is not difficult as they send up suckers whenever you prune the top). When the sucker had grown past the point I needed the branch I bored a hole completely through the trunk with an electric drill, just big enough so that the sucker would pass through without damage. I removed the leaves from the sucker being careful not to damage the small buds at the base of each leaf. I then carefully threaded the sucker through the hole in the trunk. I packed the in and out holes with Blue Tac to stop the cambium from drying out and tied the sucker in place with some strips of old stocking. (the stocking is stretchie and will not cut into the new branch). Now it is just a matter of growing the sucker as much as possible. Let it grow four or five times longer than you want then cut off the end shoot. This encourages side branching which will fatten the branch faster. If you keep removing the end buds from side branches on the protruding sucker you will get more side branches and better reticulation.
You can tell when the graft has taken as the sucker will swell where it leaves the trunk and be thicker than where it enters. This process may take several seasons and it is better to leave it too long than not long enough. Using branch cutters cut through the sucker where it enters the trunk and at ground level. The branch can now be carefully wired and shaped.
The advantages of this method of grafting are that the sucker is completely compatible and there is little relative movement between the tree and the sucker (also it works).
To date I have used this method on four Privets and two Figs and have had total success. Plants must be healthy and growing vigorously. I highly recommend the method and have been able to enhance the appearance of my trees.