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Computed tomography (CT) is a powerful non-invasive tool to analyze cultural heritage objects by allowing museum professionals to obtain 3D information about the objects' interior. These insights can help with the conservation or restoration of the objects, as well as provide contextual information on the objects' history or making process. Cultural heritage objects exist in a wide variety and have characteristics which present challenges for CT scanning: multi-scale internal features, a diversity of sizes and shapes, and multi-material objects. Because X-ray absorption is related to the density, thickness of the material, and atomic composition, the challenges are greater when the object consists of multiple different materials with varying densities. This is especially true for cases with extreme density contrasts such as that between metals and textiles. An untailored acquisition of CT scans of multi-material objects can lead to reduced image quality and heavy visual errors called image artifacts, which can influence the perception or representation of information. A tailored acquisition can reduce these artifacts and lead to a higher information gain. In this work, we firstly discuss how the X-ray beam properties and the beam-object interaction influence CT image formation and how to use filters to manipulate the emitted X-ray beam to improve image quality for multi-material objects. We showcase that this can be achieved with limited resources in a low-cost DIY fashion with thin sheets of metal as filters, 3D-printed filter frames and a filter holder. Secondly, we give a qualitative analysis of the influence of the CT acquisition parameters illustrated with two case study objects from the textile collection of the Rijksmuseum, Amsterdam, The Netherlands. With this we provide insights and intuitions on tailoring the CT scan to the cultural heritage objects. Thirdly, we extract a general concept of steps for museum professionals to design an object-tailored CT scan for individual cases. [ABSTRACT FROM AUTHOR]