  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)
