Dead center cup

[Charley Davidson]

After reading about one of these I actually had a need for it last night so I made a quick & dirty version, it mounts in my drill chuck & I used white lith grease worked great

 

[Tony Wells]

A similar tip for turning small diameter < 3/16 or so stock with a center is to turn a point on it @ 60 degrees, and take a tap with a center hole in the shank end of it. Chuck it in your tailstock chuck and run it against the stock with a bit of lube. Of course, small diameter stock will flex, so very little pressure should be used. And of course, length must be allowed to face off the point after you're done.