We have a table with about 2 million rows (and growing) in it and we
need to access the data in
the table for customer support queries. There are 3 main fields that
are used to identify the data
for the customer query, namely:

LogDate TIMESTAMP
Field1 VARCHAR(21)
Field2 VARCHAR(21)

The SQL statement looks something like this

select "Id","LogDate","Field3" from "TableName"
where ("LogDate" BETWEEN 'Date1' and 'Date2') AND
(("Field1"='String1') OR ("Field2"='string1'))
order by "LogDate"

I am using a composite descending index on the 3 fields,
ie "LogDate","Field1","Field2" and I am
not getting the performance that I need. There will never be more
than 5 records that share the
same "LogDate" value, but there could be a lot of duplicate data in
the other 2 fields

Are composite indexes the best way to go in this case?