I often make cupcakes using cupcake liners in cupcake pans. When baked there is always a "rim" around the edge of the cupcakes that I have to trim off, in order for a good appearance and to do a swirl of icing. I have tried using less batter for each cupcake, but to no avail. Is there a secret to avoiding this?

Not sure what to tell you but here's a bump!

less less batter. There is a point at which this won't happen, you just haven't gotten there yet