Invited talks are important for moving up the academic ladder, so I'd like to know how one maximizes the odds of being offered to be an invited speaker at conferences.
I am aware of the most obvious things like having important results to report. However, apparently this is not always necessary: one often sees in the list of invited speakers some fresh PhDs neighboring the really big shots. So, are there any non-obvious strategies to increase the odds of becoming an invited speaker at a conference?
I realize that the advice may be field-specific, and I am most interested in the tips for conferences in mathematics and physics.