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

SQL> create table t (id integer) partition by range (id) (partition p1 values less than (100),
  2  partition p2 values less than (maxvalue));

Table created.

SQL> create index t_i on t(id) local;

Index created.

SQL> alter index t_i rebuild compress;
alter index t_i rebuild compress
            *
ERROR at line 1:
ORA-14086: a partitioned index may not be rebuilt as a whole


SQL> alter index t_i rebuild partition p1 compress;
alter index t_i rebuild partition p1 compress
*
ERROR at line 1:
ORA-28659: COMPRESS must be specified at object level first


SQL> select * from v$version;

BANNER
--------------------------------------------------------------------------------
Oracle Database 11g Enterprise Edition Release 11.2.0.3.0 - Production
PL/SQL Release 11.2.0.3.0 - Production
CORE    11.2.0.3.0      Production
TNS for 32-bit Windows: Version 11.2.0.3.0 - Production
NLSRTL Version 11.2.0.3.0 - Production