Because the formation of protostars is believed to be closely tied to the angular momentum problem of star formation, characterizing the properties of the youngest disks around Class 0 objects is crucial. However, not much is known on the structure of the youngest protostellar envelopes, on the small scales at which disks and multiple systems are observed around more evolved YSOs, due to a lack of comprehensive high angular resolution observations (probing <100 AU). In order to tackle this issue, we conducted a large observing program with the IRAM Plateau de Bure interferometer (PdBI): the CALYPSO survey, providing us with detailed maps of molecular lines and millimeter continuum emission, probing scales down to ~30–50 au towards a sample of 17 Class 0 protostars. Here we present our analysis of the CALYPSO dust continuum emission maps, constraining disk properties of the Class 0 protostars in our sample. We show that large, r > 50 au, disk structures are not observed in most Class 0 protostars from our sample, which can be described by various envelope models reproducing satisfactorily the intensity distribution of the dust emission at all scales from 50 au to 5000 au.