Receiving mail with Amazon SES doesn't work because the MX record resolves to the CNAME I set up for Cloudfront

To receive mail with Amazon SES you need to set up an MX record to point to an SES server for your domain, but if you use CloudFront (or a load balancer, I believe) you also have to set up a CNAME that points to the host of the CloudFront distribution (or load balancer). But as I understand it DNS does not allow you to have an MX record on a host if there is also a CNAME on that host. If you ask for the MX record it returns the host pointed to by the CNAME, in my case a CloudFront distribution. Is there a way around this?