Oracle privileges and alter table.

I have a user for which I granted the alter any table privilege to. This privilege lets them alter the table columns, but it doesn't seem to allow them to add a primary key or constraint to the table. Is there a different privilege that I need to grant them to let them do this? I have searched the Oracle documents but after an hour I still haven't found the section that explains what each privilege does.

Thanks very much!

Oracle version 10.1.0.4.0
AIX 5.3

grant create any index to <user> <with admin option>;