Select Feynman diagrams for 2-loop QED vertex correction

I am trying to calculate the 2-loop correction for a basic vertex in QED

So I need to figure out what diagrams I need to consider. My literature says (without much explanation), that there are 7 contributing diagrams (including pictures). But naively it is possible to draw many more 2-loop diagrams with two electron-legs and one photon leg. Most of them are excluded by simple rules such as

1. All legs should be amputated.
2. The diagram should be connected (i.e. no vacuum bubbles).