Table JOIN causes FULLSCAN despite of indeces

[Denis]

I've a problem
There're couple of tables:

CREATE TABLE `items` (
  `id` int(11) unsigned NOT NULL auto_increment,
  PRIMARY KEY  (`id`),
  UNIQUE KEY `id` (`id`)
) ENGINE=MyISAM;

and

CREATE TABLE `rates` (
  `id` int(11) unsigned NOT NULL,
  `rate` int(11) NOT NULL default '0',
  PRIMARY KEY  (`id`),
  UNIQUE KEY `id` (`id`)
) ENGINE=MyISAM;

Execution of this query:

SELECT `rate` FROM `rates` LEFT JOIN `items` USING (`Id`)

Sometimes takes more than 2 seconds on a rather good server on both tables having about 30'000 rows
EXPLAIN shows following:

id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
1	SIMPLE	rates	ALL					33168	""
1	SIMPLE	items	eq_ref	PRIMARY,id	PRIMARY	4	mydreams.rates.id	1	Using index

i.e. we have a full rows scan,
Than I create a composite index with `rates`.`id` и `rates`.`rate` columns result is not much better:

id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
1	SIMPLE	rates	index		rateid	8		33168	Using index
1	SIMPLE	items	eq_ref	PRIMARY,id	PRIMARY	4	mydreams.rates.id	1	Using index

DB: MySQL 5.0.22 (win32) and MySQL 5.0.26 (OpenSuSE)

Help me please.