Miniaturized weak affinity chromatography is emerging as an interesting alternative to conventional biophysical tools for performing fragment-screening studies in the context of fragment-based drug discovery. In order to push back the analytical limits, it is necessary not only to control non-specific interactions with chromatographic support, but also to adapt this methodology by comparing the results obtained on an affinity column to a control column. The work presented in this study focused on fragment screening that targets a model membrane protein, the adenosine A2A receptor, embedded in nanodiscs (NDs) as biomimetic membranes. By studying the retention behavior of test fragment mixtures on supports modified with different types of NDs, we were able to determine the contribution of ND-related non-specific interactions, in particular the electrostatic effect of anionic phospholipids and the hydrophobic effect of neutral phospholipids. Different strategies for the preparation of control columns (empty NDs, orthosteric site blocking) were investigated and are presented for the first time. With these two types of control columns, the screening enabled the identification of two new fragments of AA2AR, which were confirmed by competition experiments and whose Kd values, estimated directly during the screening or after the competition experiments in frontal mode, were in good agreement.