Aims. We present photometric data of debris disks around HIP 103389 (HD 199260), HIP 107350 (HN Peg, HD206860), and HIP 114948 (HD 219482), obtained in the context of our Herschel Open Time Key Program DUNES (DUst around NEarby Stars). Methods. We used Herschel/PACS to detect the thermal emission of the three debris disks with a 3 sigma sensitivity of a few mJy at 100 um and 160 um. In addition, we obtained Herschel/PACS photometric data at 70 um for HIP 103389. Two different approaches are applied to reduce the Herschel data to investigate the impact of data reduction on the photometry. We fit analytical models to the available spectral energy distribution (SED) data. Results. The SEDs of the three disks potentially exhibit an unusually steep decrease at wavelengths > 70 um. We investigate the significance of the peculiar shape of these SEDs and the impact on models of the disks provided it is real. Our modeling reveals that such a steep decrease of the SEDs in the long wavelength regime is inconsistent with a power-law exponent of the grain size distribution -3.5 expected from a standard equilibrium collisional cascade. In contrast, a very distinct range of grain sizes is implied to dominate the thermal emission of such disks. However, we demonstrate that the understanding of the data of faint sources obtained with Herschel is still incomplete and that the significance of our results depends on the version of the data reduction pipeline used. Conclusions. A new mechanism to produce the dust in the presented debris disks, deviations from the conditions required for a standard equilibrium collisional cascade (grain size exponent of -3.5), and/or significantly different dust properties would be necessary to explain the potentially steep SED shape of the three debris disks presented. (abridged)
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