Pigeon proof bird feeder

Hi there!

I hope all of you are having a spectacular day. We have an issue with our bird feeder originally intended for the tits and occasionally a woodpecker.

As a disclaimer, by itself I don’t have any problem with pigeons, and I feel so sorry for them. However since they noticed the bird feeder they always fly to our windowsil/ outer part of the AC, they shit everywhere and not only scare the tits away, but also pour out all the food from the feeder, technically making it pointless to have it out in the first place.

Did anybody have an issue similar to this? Is there anything I can do to still feed the small birds, but make it inaccessible for the pigeons? (We live in the city so the pigeons could get more than enough food).

Thank you for your help🤗