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Radiotherapy with heavy ions, in particular, 12C beams, is one of the most advanced forms of cancer treatment. Sharp dose gradients and high biological effectiveness in the target region make them an ideal tool to treat deep-seated and radioresistant tumors, however, at the same time, sensitive to small errors in the range prediction. Safety margins are added to the tumor volume to mitigate these uncertainties and ensure its uniform coverage, but during the irradiation they lead to unavoidable damage to the surrounding healthy tissue. To fully exploit the benefits of a sharp Bragg peak, a large effort is put into establishing precise range verification methods for the so-called image-guided radiotherapy. Despite positron emission tomography being widely in use for this purpose in 12C ion therapy, the low count rates, biological washout, and broad shape of the activity distribution still limit its precision to a few millimeters. Instead, radioactive beams used directly for treatment would yield an improved signal and a closer match with the dose fall-off, potentially enabling precise in vivo beam range monitoring. We have performed a treatment planning study to estimate the possible impact of the reduced range uncertainties, enabled by radioactive 11C beams treatments, on sparing critical organs in the tumor proximity. We demonstrate that (i) annihilation maps for 11C ions can in principle reflect even millimeter shifts in dose distributions in the patient, (ii) outcomes of treatment planning with 11C beams are significantly improved in terms of meeting the constraints for the organs at risk compared to 12C plans, and (iii) less severe toxicities for serial and parallel critical organs can be expected following 11C treatment with reduced range uncertainties, compared to 12C treatments.