Large-scale code reuse significantly reduces both development costs and time. However, the massive share of third-party code in software projects poses new challenges, especially in terms of maintenance and security. In this paper, we propose a novel technique to specialize dependencies of Java projects, based on their actual usage. Given a project and its dependencies, we systematically identify the subset of each dependency that is necessary to build the project, and we remove the rest. As a result of this process, we package each specialized dependency in a JAR file. Then, we generate specialized dependency trees where the original dependencies are replaced by the specialized versions. This allows building the project with significantly less third-party code than the original. As a result, the specialized dependencies become a first-class concept in the software supply chain, rather than a transient artifact in an optimizing compiler toolchain. We implement our technique in a tool called DepTrim, which we evaluate with 30 notable open-source Java projects. DepTrim specializes a total of 343 (86.6%) dependencies across these projects, and successfully rebuilds each project with a specialized dependency tree. Moreover, through this specialization, DepTrim removes a total of 57,444 (42.2%) classes from the dependencies, reducing the ratio of dependency classes to project classes from 8.7x in the original projects to 5.0x after specialization. These novel results indicate that dependency specialization significantly reduces the share of third-party code in Java projects.