Matthew Weier O'Phinney has posted an article to his site showing you how to fix version issues in branches when using Composer packages and libraries in your applications.
For the Zend Framework component repositories, we occasionally need to backport changes to the 2.4 LTS releases. This requires checking out a branch based off the last LTS tag, applying patches (often with edits to translate PHP 5.5 syntax to PHP 5.3), and running tests against PHP 5.3 and 5.4.
Of course, to run the tests, you need the correct set of dependencies installed. If you have any component dependencies, that means running a composer update to ensure that you get the 2.4 versions of those components. And that's where my story begins.
He talks about some of the issues he's come across when testing components and Composer, not understanding that the environment has changed, does not load the correct versions of the necessary libraries. He first tried to fix the dependencies himself, adjusting the version numbers required but with no luck. Finally he stumbled across something on the Composer site that helped: the ability to define a "root version" environment variable that made it adhere to the versions he needed.