SQL & PL/SQL

I have a query that appears perform better when not using a specific index (my_index). However other queries do appear to benefit from this index.

If I do an explain on the query it shows “INDEX FAST FULL SCAN my_index”
This query uses my_table in the outer query as well as an inner query.

In an attempt to stop my_index being used I have tried the NO_INDEX hint and functions. For example, the following syntax when tried on both queries did not work.

Select /*+NO_INDEX(my_table)*/ my_table.my_column from … .

Select /*+NO_INDEX(my_table my_index)*/ my_table.my_column from …

Is their a problem with the NO_INDEX hint ?
Are their conditions where the NO_INDEX hint is ignored ?

The indexed columns are CHAR(10) and CHAR(10) and trying to invalidate the Index by using a function also did not work, such as

…. where TRIM(my_table.my_column_a) in (‘EXECUTED’,’NOTEXECD’)
and TRIM(my_table.my_column_b) in (‘VERIFIED’,’NOTVERIF’) …
and ….

But this also does not work.

Any other suggestions as to how I might be able to turn if the use of my_index for this query?
I would post the actual SQL but I am at a customer site and they are very concerned about anything being sent out of their network.