Thank you, Rosie. The bases are not wooden, drilling them would crack or break them. This has been my challenge on these two. For glass ones, drilling is not an option either. I made a beautiful one that I sold twice and had to take back the sale as the bottom came loose from the large platter. So, I remade it and it seemed fine so I sold it again! Then as I was loading it into the person's car (it was tall and intricate), it 'snapped' and not where I glued it. I guess I torqued it somehow as I was attempting to get it into the backseat of a two door car. Sigh.
You can see it in this picture, it's the tall birdbath to the left of center.
This one, I've never had any worries about it toppling as it has a broad enough base on it. It's to the right of center with the floral, ceramic bath on top.