Rails 4.0.2 dependency mime-types (~> 1.16) is conflicting with other tools using mime-types 2.0

When trying to install the Mechanize gem, I get the following error:

Resolving dependencies...
Bundler could not find compatible versions for gem "mime-types":
  In Gemfile:
    rails (= 4.0.2) ruby depends on
      mime-types (~> 1.16) ruby

    mechanize (~> 2.7.3) ruby depends on
      mime-types (2.0)

Now I understand that it's because rails depends on mime-types ~1.16 and Mechanize mime-types 2.0 but is there no way to get those two to play nicely together?