When we moved to our new rental home there were 2 large trash bins and an equally large recycling bin in the garage. They were huge and we were a little short on space in the garage as is was. Our family of 5 has never filled one bin except on rare occasions when we end up with boxes or lawn trash. Even when we had diapers in the house we had one "dumpster". And here is how we do it.
We collapse everything!
My husband spent time growing up in a military family on a base in another country where they had to ration their trash to one can. When we got married, I started doing this too. It just makes sense.
Here is an example of something that takes up space and doesn't have to. Pop-tart boxes aren't that big but when you place them into the trash can along with cereal boxes, milk cartons, etc. they take up lots of space.
Those big 12 pack soda boxes take up an inordinate amount of space until you rip them apart and/or collapse them. 2 liter bottles can be collapsed by taking off the lid and squeezing the air out then replacing the lid. We don't take out the trash more than once every 2 days or so.
And we had the trash and recycling guys come and pick up the extra bins which made more space in the garage!
Here is the flattened Pop-tart box for reference. It's almost flat! That takes up almost no space.
Get the kids involved. Especially if they are the ones taking out the trash. Take your aggression out on the boxes and stomp on them. See if you can get your trash down to one can!