Setting file contexts on /proc files

I want to restrict access to files in /proc as much as possible using SELinux. When I try to chcon a directory in /proc, it fails:

$ chcon -t staff_proc_t /proc/acpi
chcon: failed to change context of '/proc/acpi' to ‘system_u:object_r:staff_proc_t’: Operation not supported

Apparently, the /proc filesystem does not allow changing the context directly. How can I set SELinux contexts on /proc entries? If that is not possible, I would like to prohibit access to these files by other means. I would like to hide mountpoint information, ACPI directory, /proc/config.gz etc.