Now Tiny Tim is stabilized. My glass was too large for the little fellow but lucky me I'm an expert on buying odd stuff, so I managed to find a small clear plastic box of perfect size, put Tiny T (pot and all) into the box and then put both of them into the glass. The irony of it all is that the plastic box originally contained one of my IQ-puzzles.
Now I can't knock the little Phal over and it's as stable as a rock! Or at least as an equestris in an unstable pot put into a small box put into a glass.
Of course I had to take some photos of my ingenious solution and show you.