In-beam positron emission tomography (in-beam PET) is currently the only method for an in situ monitoring of highly tumour-conformed charged hadron therapy. At the experimental carbon ion tumour therapy facility, running at the Gesellschaft für Schwerionenforschung, Darmstadt, Germany, all treatments have been monitored by means of a specially adapted dual-head PET scanner. The positive clinical impact of this project triggered the construction of a hospital-based hadron therapy facility, with in-beam PET expected to monitor more delicate radiotherapeutic situations. Therefore, we have studied possible in-beam PET improvements by optimizing the arrangement of the γ-ray detectors. For this, a fully 3D, rebinning-free, maximum likelihood expectation maximization algorithm applicable to several closed-ring or dual-head tomographs has been developed. The analysis of β⁺-activity distributions simulated from real-treatment situations and detected with several detector arrangements allows us to conclude that a dual-head tomograph with narrow gaps yields in-beam PET images with sufficient quality for monitoring head and neck treatments. For monitoring larger irradiation fields, e.g. treatments in the pelvis region, a closed-ring tomograph was seen to be highly desirable. Finally, a study of the space availability for patient and bed, tomograph and beam portal proves the implementation of a closed-ring detector arrangement for in-beam PET to be feasible.