In single host mode (no swarm and more complicated stuff) I have a host with multiple public IPs. It seems there is no way to configure which of those IPs containers use for outbound communication. Always the primary IP on the host is used. So I would need that different containers are seen on the Internet as using different IPs.

My use case is a mail server. I have an extra IP allocated to the server to use for sending e-mails so that forward and backwards DNS entries can match. The other IP address is used for HTTP virtual hosting and has many different DNS entries. Additionally using an extra IP for a dedicated mail server is in general a good practice.

Tried with Docker 1.12.5 on Linux (Ubuntu 16.04.1 LTS) with 4.8.0 kernel.