Sub-millimeter functional imaging has the potential to capture cortical layer-specific functional information flow within and across brain systems. Recent sequence advancements of fMRI signal readout and contrast generations resulted in wide adaptation of layer-fMRI protocols across the global ultra high-field (UHF) neuroimaging community. However, most layer-fMRI applications are confined to one of ≈100 privileged UHF imaging centers, and sequence contrasts with unwanted sensitivity to large draining veins. In this work, we propose the application of vein-signal free vascular space occupancy (VASO) sequences at widely accessible 3T scanners. Specifically, we implement, characterize, and apply a cerebral blood volume (CBV)-sensitive VASO fMRI at a 3T scanner setup, as it is typically used in the majority of cognitive neuroscience and clinical neuroscience fMRI studies. We find that the longer T2*, and stronger relative T1 contrast at 3T can account for some of the lower z-magnetization in the inversion-recovery VASO sequence compared to 7T and 9.4T. In the main series of experiments (N=16), we test the utility of this setup for motor tasks and find that -while being limited by thermal noise- 3T layer-fMRI VASO is feasible within conventional scan durations. In a series of auxiliary studies, we furthermore explore the generalizability of the developed protocols for a larger range of study designs including: visual stimulation, whole brain movie watching paradigms, and cognitive tasks with weaker effect sizes. We hope that the developed imaging protocols will help to increase accessibility of vein-free layer-fMRI imaging tools to a wider community of neuroimaging centers.