can you lease a used car? need something bigger as my small car is not cutting it with DS, toys, stroller ,etc....I am caving in, 2 years later, LOL!

I don't want to but but I don't necessarily want to lease the brand new model? I've never really heard of it or known anyone that has. I don't travel far so a lease would be great for me but I want to keep my payments reasonable so don't need the latest model.....anyone know or does it vary by type of car? I am clueless...