Improve performance on SQL Server Query
I would suggest to try an index like this:

CREATE NONCLUSTERED INDEX NCI_ProcessState_ProcessStateDateLastModified_SleepUntil 
ON [TABLE](ProcessState,ProcessStateDateLastModified,SleepUntil)


This way you can filter sharp on the state as all others will result in bigger result sets due to the &lt;= filter.

You can check the index usage easily with this query:

SELECT obj.*,usage.*
FROM sys.dm_db_index_usage_stats AS usage
INNER JOIN sys.indexes as obj
        ON usage.object_id = obj.object_id
WHERE database_id = db_id()


Just filter it on your index and take a look a the search and update columns.