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[Display omitted] Computed Tomography (CT) has proven itself as a powerful technique for analysing the internal structure of cultural heritage objects. The process followed by conservators and technical art historians for investigating an object is explorative: each time a new question is asked based on the outcome of the previous investigation. This workflow however conflicts with the static nature of CT imaging, where the planning, execution and image analysis for a single CT scan can take days, or even weeks. A new question often requires conducting a new experiment, repeating the process of planning, execution and image analysis. This means that the time that is needed to complete the investigation is often longer than originally anticipated. In addition, it brings up more practical challenges such as the transportation of the object, facility availability and dependence on the imaging operator, as well as the cost of running additional experiments. A much needed interactive imaging process, where the user can adapt the CT scanning process based on the insights discovered on the spot, is hard to accomplish. Therefore, in this paper we show how a time-efficient explorative workflow can be created for CT investigation of art objects, where the object can be inspected in 3D while still in the scanner, and based on the observations and the resulting new questions, the scanning procedure can be iteratively refined. We identify the technical requirements for a CT scanner that can address the diversity in cultural heritage objects (size, shape, material composition), and the need for adaptive steering of the scanning process required for an explorative workflow. Our approach has been developed through the interdisciplinary research projects The See-Through Museum and Impact4Art. We demonstrate the key concepts by showing results of art objects scanned at the FleX-ray Laboratory at CWI, Amsterdam. [ABSTRACT FROM AUTHOR]