Today I found myself in a situation where I needed to compress an already existing, partitioned index.  First I issued an alter table to rebuild and compress the whole index:

SQL> ALTER INDEX MY_INDEX REBUILD COMPRESS;
ERROR at line 1:
ORA-14086: a partitioned index may not be rebuilt as a whole

So next I tried to rebuild compress one of the partitions:

SQL> ALTER INDEX MY_INDEX REBUILD PARTITION PART1 COMPRESS;
ERROR at line 1:
ORA-28659: COMPRESS must be specified at object level first

Turns out that there is no way you can do a rebuild compress on partitioned indexes.  I did not realize that until I stumbled across document 312843.1 on Metalink.  It says the only way to compress a partitioned index is to drop it and recreate it (through 11.2).