How to increase the odds of becoming an invited speaker at science conferences? 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.
Give some colloquia (departmental seminars or lab-specific talks) in the departments of organizers of conferences. You can sometimes invite yourself by writing to the organizer of their seminar series and offering yourself as a speaker but better might be having your phd advisor write and recommend you.

This will increase your name recognition with the critical people and can give you a reputation for giving good talks. Organizers are unlikely to take a chance on someone that is junior and none of them have heard speak. If you can give a talk somewhere that will be videoed and posted online, that would also help with this issue.

Finally, if you work with a more famous friend (or phd advisor) in the same area who is frequently invited to give talks, you could mention to them that you are trying to do this and they may recommend you for talks they have to decline.