Thanks for the reply Benjamin!
Sorry for taking so long to get back. I thought I got it right when I got the document list with the below mentioned method. But when I took a closer look I still was stuck.
If i use /documents/ I get a 404 from the server (not the WordPress 404!). I guess this is a question of permalink settings… If I use ?post_type=document instead I can see the document list. Both private/public (while logged in) and public (not logged in).
But, when it comes to shortcodes I get only public documents from the shortcode [documents].
I am also using the Members plugin and custom categories for the documents. If that matters…