I don't very often promote specific vendor's products, but in this instance I want to make an exception. I have been using the Valentino Synthetic self-adhesive neck corks in my repair work for several years now and I am impressed at how well they perform and how well they hold up. Besides the ease of installation, the feature of this neck cork I like the most is that it allows the player to use mouthpieces with different size shanks interchangeably. Once the smaller mouthpiece is removed, the synthetic material expands to create a snug fit for the larger one. The only downside to this product is that it costs a bit more than natural cork. This video shows a demonstration on how to install the cork. The tricky part is to cut a straight line at the seam, but the "cork" has enough flex that you can squeeze the sides closer together if you are a little bit off.