Proton computed tomography (pCT) has high accuracy and dose efficiency in producing spatial maps of the relative stopping power (RSP) required for treatment planning in proton therapy. With fluence-modulated pCT (FMpCT), prescribed noise distributions can be achieved, which allows to decrease imaging dose by employing object-specific dynamically modulated fluence during the acquisition. For FMpCT acquisitions we divide the image into region-of-interest (ROI) and non-ROI volumes. In proton therapy, the ROI volume would encompass all treatment beams. An optimization algorithm then calculates dynamically modulated fluence that achieves low prescribed noise inside the ROI and high prescribed noise elsewhere. It also produces a planned noise distribution, which is the expected noise map for that fluence, as calculated with a Monte Carlo simulation. The optimized fluence can be achieved by acquiring pCT images with grids of intensity modulated pencil beams. In this work, we interfaced the control system of a clinical proton beam line to deliver the optimized fluence. Using three phantoms we acquired images with uniform fluence, with a constant noise prescription, and with an FMpCT task. Image noise distributions as well as fluence maps were compared to the corresponding planned distributions as well as to the prescription. Furthermore, we propose a correction method that removes image artifacts stemming from the acquisition with pencil beams having a spatially varying energy distribution that is not seen in clinical operation. RSP accuracy of FMpCT scans was compared to uniform scans and was found to be comparable to standard pCT scans. While we identified technical improvements for future experimental acquisitions, in particular related to an unexpected pencil beam size reduction and a misalignment of the fluence pattern, agreement with the planned noise was satisfactory and we conclude that FMpCT optimized for specific image noise prescriptions is experimentally feasible.