Indexes and optimization

I'm not brilliant when it comes to going beyond the basics with MySQL, however, I'm trying to optimize a query:

SELECT DATE_FORMAT(t.completed, '%H') AS hour, t.orderId, t.completed as stamp,
       t.deadline as deadline, t.completedBy as user, p.largeFormat as largeFormat 
    FROM tasks t
    JOIN orders o ON o.id=t.orderId
    JOIN products p ON p.id=o.productId
    WHERE DATE(t.completed) = '2013-09-11'
    AND t.type = 7
    AND t.completedBy IN ('user1', 'user2')
    AND t.suspended = '0'
    AND o.shanleys = 0
    LIMIT 0,100

+----+-------------+-------+--------+----------------------------+-----------+---------+-----------------+-------+-------------+
| id | select_type | table | type   | possible_keys              | key       | key_len | ref             | rows  | Extra       |
+----+-------------+-------+--------+----------------------------+-----------+---------+-----------------+-------+-------------+
|  1 | SIMPLE      | o     | ref    | PRIMARY,productId,shanleys | shanleys  | 2       | const           | 54464 | Using where |
|  1 | SIMPLE      | p     | eq_ref | PRIMARY                    | PRIMARY   | 4       | sfp.o.productId |     1 |             |
|  1 | SIMPLE      | t     | ref    | NewIndex1                  | NewIndex1 | 5       | sfp.o.id        |     6 | Using where |
+----+-------------+-------+--------+----------------------------+-----------+---------+-----------------+-------+-------------+

Before some of the indexes were added it was performing full table scans on both the p table and the o table.

Basically, I thought that MySQL would:

limit down the rows from the tasks table with the where clauses (should be 84 rows without the joins)

then go through the orders table to the products table to get a flag (largeFormat).

My questions are why does MySQL look up 50000+ rows when it's only got 84 different ids to look for, and is there a way that I can optimize the query?

I'm not able to add new fields or new tables.

Thank you in advance!