With the advance of smart IoT devices (Internet of Things) the amount of valuable data will increase dramatically. With its recently enacted Data Act (DA) the EU introduces new data access and sharing rights for the users of IoT devices. This article analyzes how the DA will change the bundle of rights on non-personal IoT data regarding who can control, access, use, share, and monetize this data. In a first step, we apply the property rights theory (esp. the approach of Barzel) for explaining the status quo of IoT data governance. Here the manufacturers can get through the technical design of their IoT devices exclusive de facto control over IoT data ("capture" of data). In a second step, we analyze how the DA changes this de facto bundle of rights in order to unlock more IoT data for innovation, competition, and empowerment of users. Since the DA is not very clear and partly contradictory, three different concepts for the design of this bundle of rights are analyzed and compared: A data holder-centric IP-like concept, a user-centric concept, and the concept of co-generated data. The article analyzes all three concepts from an economic perspective including relevant market failures regarding IoT data in B2B and B2C contexts. For achieving the objectives of the DA, especially regarding unlocking of data for innovation, bundles of rights should be chosen which reject notions of exclusivity and enable broad access and sharing of IoT data. The enacted Data Act, which still clings too much to the exclusivity of data and includes too many hurdles for data sharing, cannot be expected to contribute much to achieving these objectives.