Can I set a users profile image using the Facebook API?

I'm looking for a user.setImage call or something to that effect on the Facebook API but I can't see anything to achieve this: specifically to overwrite a user's profile image (not just post an image on their wall).

I can't see anything in the docs. Do you know if this is possible and if so any docs on implementing it?

You can redirect the user to the following link where [PID] stands for the id of the desired picture:

http://www.facebook.com/photo.php?fbid=[PID]&makeprofile=1

On this page the user will see the picture and immediately be prompted with a dialog if he wants to set it as his profile picture.

No, you cannot.

From the photos.Upload documentation:

However, you cannot upload to a user's profile picture album.

Checkout my answer in this thread: how to set a facebook profile picture using the graph api

You can't set the profile picture, but you can upload it to an album, and then send the user to the "make profile picture"-page for that picture.

There must be a hidden API because the iphone facebook app does it... Maybe you can discover how by setting a proxy between an iphone and Facebook and decipher it... or the API may be restricted to only Facebook's own apps...