Issues converting MyISAM table to InnoDB (auto column issue)

Question

I'm having issues trying to convert a table from MyISAM to InnoDB in MySQL 5.6.

The following is the table dump:

--
-- Table structure for table `companies`
--

DROP TABLE IF EXISTS `companies`;
/*!40101 SET @saved_cs_client     = @@character_set_client */;
/*!40101 SET character_set_client = utf8 */;
CREATE TABLE `companies` (
  `uid` int(20) NOT NULL,
  `cid` int(20) NOT NULL AUTO_INCREMENT,
  `cname` varchar(500) NOT NULL,
  `rfc` varchar(20) NOT NULL,
  `address` varchar(1000) NOT NULL,
  `dbUseExternal` tinyint(1) NOT NULL DEFAULT '0',
  `dbHost` varchar(50) NOT NULL,
  `dbPort` varchar(50) NOT NULL,
  `dbUser` varchar(50) NOT NULL,
  `dbPass` varchar(50) NOT NULL,
  `dbSSL` varchar(50) NOT NULL,
  `dbDriver` varchar(50) NOT NULL,
  `dbName` varchar(50) NOT NULL,
  `status` int(10) NOT NULL,
  PRIMARY KEY (`uid`,`cid`)
) ENGINE=MyISAM DEFAULT CHARSET=latin1;
/*!40101 SET character_set_client = @saved_cs_client */;

It works as MyISAM. But, if I try to convert it to InnoDB (or if I try editing this dump to insert it on the command line as a sql file), I get the following error:

Incorrect table definition; there can be only one auto column and it must be defined as a key

I understand that error - or at least I thought I did. I'm not really using more than one AUTO_INCREMENT column and it is defined as primary key.

Also, the information I've found regarding the error is always because of an obvious missing key or a duplicate AUTO_INCREMENT definition. One more thing I see generally commented is that the same is true for MyISAM and InnoDB.

So, why does it work for MyISAM and not for InnoDB?

Thanks in advance for any comments.

Francisco