We propose to carry out full-synthesis (12-h) HI ATCA observations of 8 bright Blue Compact Dwarf Galaxies (BCDGs), for which we have already got interesting results. Some are apparently isolated, others belong to galaxy groups. We want to estimate the distribution of the HI in each BCDG and its surrounding, looking for independent HI clouds or morphological features that reveal interaction processes. We will also analyze the kinematics of the neutral gas and, using 1.4 GHz radio continuum maps, derive an extinction-free star formation rate. We will combine the data with the results obtained using UV/optical/NIR images and spectroscopy. We remark that 4 of the galaxies have been observed at the 8.2m VLT and 5 will be observed at the 10.4m GTC and the Herschel observatory.