That is how I do it: lid under the container, then the next smaller lid
inside it and the matching container on top of that lid.

I do have one set of bowls and covers that can nest inside one another with
the covers on. They're for Passover, meaning that they're used only about 8
days a year. Nesting with covers on seems inconvenient for containers that
get used frequently; wouldn't it be annoying to have to open several
containers before you could reach the smallest one?

> Am I the only one who does this? I nest them, with the lid UNDER the
> container. So I take my big huge lid, and put it on the shelf. Then the
> big huge container sits on top of it.
>
> Into that, I put the medium lid, with the medium container on top of it.
>
> And so on.
>
> They nest, AND the lids stay with the proper container so I need not
> search for the right lid.
>
> I have three stacks: One for the square containers, one for the rounds,
> and one for the oblongs.