Linux distributions often include package management tools such as apt-get in Debian or yum in RedHat. Using information about package dependencies and conflicts, such tools can determine how to install a new package (and its dependencies) on a system of already installed packages. Using off-the-shelf SAT solvers, pseudo-boolean solvers, and Integer Linear Programming solvers, we have developed a new package-management tool, called Opium, that improves on current tools in two ways: (1) Opium is complete, in that if there is a solution, Opium is guaranteed to find it, and (2) Opium can optimize a user-provided objective function, which could for example state that smaller packages should be preferred over larger ones. We performed a comparative study of our tool against Debian?s apt-get on 600 traces of real-world package installations. We show that Opium runs fast enough to be usable, and that its completeness and optimality guarantees provide concrete benefits to end users.