ABSTRACT In this work, we analyse three average-luminosity hard X-ray selected AGN: ESO 506-G27, IGR J19039+3344, and NGC 7465. They have simultaneous Swift/XRT and NuSTAR data never published before and have been poorly studied at X-ray energies. These sources make for interesting targets both from a methodological and scientific point of view. Scientifically, they are of interest since they are possibly heavily absorbed objects, belong to a peculiar class and are variable both in flux and in spectral shape. Methodologically, because it is an interesting exercise to understand how existing spectral models can be applied to faint sources and how the use of NuSTAR data alone and then simultaneous and/or average data impacts on the spectral parameters determination. In this work, we demonstrate that simultaneous data are not sufficient if their statistical quality is poor. Moreover, we show that also the use of time-averaged data when dealing with faint AGN does not always provide confident results as for brighter AGN. Regardless of the poor data quality employed in our analysis, we are able to provide insights into the spectral characteristics of each source. We analyse in detail for the first time the iron line complex of ESO 506-G27, finding not only the presence of the iron K α and K β lines, but also of the iron K edge around 7 keV in the NuSTAR data. We also highlight changes in the absorption properties of IGR J19039+3344 and confirm NGC 7465 to be an unabsorbed type 1 LINER.