Hi Adriaan,
The way I have done it is to create some specific user groups through the user groups section found in the library.
Then for the space that you want restricted go into that space and there is a section for 'Users' top left and then just modify the groups accordingly. Be careful though that if you have any sub spaces that you may not want restricted they would automatically be applied the parent's space settings, so you would have to modify these as well if you wanted different access.
------------------------------
Darren Castle
------------------------------