composite vs single column secondary index in innodb

We have a composite primary key consisting of
column a, column b, column c. We don't have a lot of variation on
column a and it makes sense for us to cluster by a.
Our queries are
SELECT column c FROM table WHERE column a=something and column e=something.
By creating a composite secondary index on column e (column a and
column e), we're thinking we can reduce the amount of seek on the
index on column e.

My question is -
is the column a value available already as bookmark lookups on single
column index on e or would we better off creating a composite index on
a and e if we always search by a and e? We're willing to accept some
overhead on inserts for selects.

Kyong

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