Fitting a face plate to your work 

This video explains some improvements that can be made to the standard faceplate that came with your lathe to help with mounting the wood as stable as possible.
Addendum: For very hard woods such as Australian Burls it is recommended to pre-drill the holes in the timber before driving the screws. The tek screws being used are designed for wood, not the tek screws that are used for roofing.