for big nations that miss out (Sweden, Greece, Ireland, Bulgaria, Wales, Norway, etc) if you just don't let 3rd place advance. Just do eight groups, top two only get through.

And then you could make all the Malta, Gibralta, Liechtenstein, Andorra, etc. type countries get treated the way CONCACAF treats the Carribean nations. Make them go through their own round of qualifying but so that only two or three teams advance. Qualification right now knocks out ~30 teams, but the teams that advance do so by beating the Vatican City or Faroe Islands 12-0 in a group game. Make it so 8-10 of the small countries are knocked out early, and then another 10-12 in the round with the rest of the countries. 

Thank you for coming to my TED Talk.

Sincerely,

A sad fan who wants to watch Halaand and Isak at the Euros.