slow MySQL "INNER JOIN"

On a web site, I am using django to make some requests :

The django line :

CINodeInventory.objects.select_related().filter(ci_class__type='equipment',company__slug=self.kwargs['company'])

generates a MySQL query like that :

SELECT *
FROM `inventory_cinodeinventory`
INNER JOIN `ci_cinodeclass` ON ( `inventory_cinodeinventory`.`ci_class_id` = `ci_cinodeclass`.`class_name` )
INNER JOIN `accounts_companyprofile` ON ( `inventory_cinodeinventory`.`company_id` = `accounts_companyprofile`.`slug` )
INNER JOIN `accounts_companysite` ON ( `inventory_cinodeinventory`.`company_site_id` = `accounts_companysite`.`slug` )
INNER JOIN `accounts_companyprofile` T5 ON ( `accounts_companysite`.`company_id` = T5.`slug` )
WHERE (
`ci_cinodeclass`.`type` = 'equipment'
AND `inventory_cinodeinventory`.`company_id` = 'thecompany'
)
ORDER BY `inventory_cinodeinventory`.`name` ASC

The problem is that for only 40 000 entries in the main table, it takes 0.5 seconds to process.

I checked all indexes, create the ones that is required for sorting or joinning : I still have problem.

The funny thing is that if I replace the last INNER JOIN by a LEFT JOIN, the request is 10x faster ! Unfortunately, As I am using django for requesting, I do not have access to the SQL requests it generates (I do not want to do raw SQL myself).

for the last join as an "INNER JOIN" the EXPLAIN gives:

+----+-------------+---------------------------+--------+----------------------------------------------------------------------------------------------------------+------------------------------------+---------+------------------------------------------------+-------+---------------------------------+
| id | select_type | table                     | type   | possible_keys                                                                                            | key                                | key_len |