Due to recent advances in data science and Big Data the importance of data is increasing. Although service choreographies provide means to specify complex conversations between multiple interacting parties from a global perspective and in a technology-agnostic manner, they do not fully reflect the paradigm shift towards data-awareness at the moment. In this paper, we discuss current shortcomings such as missing support for data flow across services and a choreography data contract all interacting parties agree on. This results in more complex and rigid choreography models, making them also less flexible regarding their data perspective during run time. The main contribution is our approach for modeling and execution of data-aware service choreographies towards increasing the level of data awareness in choreographies.