Plane mirror convex or concave mirror which is best for bicycle mirror?

I use a mirror with a slight convex curve - like the outside of a spoon, but a lot less bent. But it's hard to find a good one. If you fasten a flat mirror most places on a bicycle, the mirror image will shake around so you can't see it. Also, in a convex mirror, you can see more of the road. But if it's too much bent, too round, then the image is distorted and you can't judge where a vehicle in the mirror really is.

The last mirror I bought was described as convex, but actually is flat, so I'm planning to get a piece of car mirror glass cut by a glazier to fit in the frame. That glass is just a little convex.

Robert Carnegie, Scotland