We are obtaining deep multiwavelength data of a sample of nearby blue compact dwarf galaxies (BCDGs) combining broad-band optical/NIR and Hα photometry, optical spectroscopy and 21-cm radio observations. Here we present HI results obtained with the Australia Telescope Compact Array for some BCDGs, all showing evident interaction features in their neutral gas component despite the environment in which they reside. Our analysis strongly suggests that interactions with or between low-luminosity dwarf galaxies or HI clouds are the main trigger mechanism of the star-forming bursts in BCDGs; however these dwarf objects are only detected when deep optical images and complementary HI observations are performed. Are therefore BCDGs real isolated systems?