I have a bit of an odd situation and I'm trying to understand it.
I have two tables, I'll list the necessary fields.
products [MyIsam -- due to full text search]  
   product_id [primary index]
Has roughly 1,000,000 rows in it.
website_products [InnoDB]  
    website_id [primary]  
    product_id [primary]
Has roughly 6,000,000 rows in it.
Now when I do queries...
SELECT
    COUNT(`product_id`)
FROM `products`
Returns in 0.109 seconds with the result "1030650"
SELECT
    COUNT(wp.`product_id`)
FROM `website_products` AS wp 
WHERE wp.`website_id` = 1133
Returns in 0.577 seconds with the result "104150"
SELECT
    COUNT(wp.`product_id`)
FROM `website_products` AS wp 
LEFT JOIN `products` AS p ON p.product_id = wp.product_id
WHERE wp.`website_id` = 1133
Returns in 38.173 seconds with result "104150"
An EXPLAIN SELECT yields:
1   SIMPLE  wp  ref PRIMARY,website_id  PRIMARY 4   const   204392  Using index
1   SIMPLE  p   eq_ref  PRIMARY PRIMARY 4   imaginer_system.wp.product_id   1   Using index
Why is it so much longer when I join the table? How can I reduce that?
 
     
    