interface - Sorting tables after multiple columns

I want to add a sorting functionality to a table. It should be able to be sorted after multiple columns.

A standard approach is something like this:

^{download bmml source – Wireframes created with Balsamiq Mockups}

But this brings one problem, no one knows, which is the first, second an third sorting key.

As an alternative I saw something like this:

^{download bmml source}

Here the position in the list implies, which is the first, second and third sort-key and the arrow show if it's asc/desc.

I think the second approach is more intuitive, but it also takes more space and I don't want the GUI to get cluttered.

Do you have some alternative ideas which would take less space?