In a new post to his site Cees-Jan Kiewiet talking about "highest" and "lowest" versions of Composer-installed libraries and testing them in Travis-CI builds.

During DPC I've had a talk with Rafael about making sure you test all your possible versions, lowest, current, and highest. The talk was ignited by the infamous composer.lock file (whether to commit it or not).

He goes on to show how you can set up a multiple-version build with the help of the "dependencies" environment variable in your ".travis.yml" configuration file. These are then used in "before_script" commands that tell the Composer install which versions to load. He includes a screenshot of the resulting build and ends with a reminder from Jordi Boggiano (lead developer of Composer) about the resources a build like this takes up and not to do it very often.