Guys, thanks for all your kind replies.

A bar-end mirror would probably solve all the problems I mentioned, but I am a little bit wary of bar-end mirrors: I always feel that I'll be running them into obstacles :-) Maybe it is not that bad ?

A small mirror that attaches to a top tube also sounds like a good idea, except that I have a step-thru bicycle.

WRT to a helmet mirror that cyccomute mentioned: is it stable enough in terms of vibrations ?