Check that the optimizer statistics are run as recommended. Identify the SQL statements that are slow. Schedule these to run at times that do not crush the rest of the system. Fix indexes that affect the bad SQL code. Check that indexes are set up for slow SQL statements.
Many times there is no index.
The index will not be as effective in comparisons. A composite index has an optimizer dependence on the 'head', the first column defined for the index. Attributes that have a small domain, uneven distribution of values and nulls are not good choices for the head attribute of a composite index. Re-ordering fields in a composite index to use a better attribute domain as an index head may help performance by magnitudes of ten. Sometimes indexes need rebuilding if they are in tables that change a lot in a short time.