Web services often impose constraints that restrict the way in which two or more input parameters can be combined to form valid calls to the service, i.e. \emph{inter-parameter dependencies}. Current web API specification languages like the OpenAPI Specification (OAS) provide no support for the formal description of such dependencies, making it hardly possible to interact with the services without human intervention. We propose specifying and automatically analyzing inter-parameter dependencies in web APIs. To this end, we propose a domain-specific language to describe these dependencies, a constraint programming-aided tool supporting their automated analysis, and an OAS extension integrating our approach and easing its adoption. Together, these contributions open a new range of possibilities in areas such as source code generation and testing.