We study the correlations of rotation velocity and absolute magnitude with surface brightness for low surface brightness dwarf irregular galaxies (dIrrs). We find that isolated objects contribute most to the scatter in the Tully–Fisher relation (TFR). Excluding these extreme cases, we develop a three-parameter (luminosity, Hi line width at 20% of peak flux level, i.e., W20, effective surface brightness) TFR for 60 dIrrs (with revised Hubble type T > 8) in the Local Volume (LV) with Cepheid and tip-of-the-red-giant-branch distance measurements. The relation is applied to galaxies of the same morphological type with radial velocities vLG ≤ 3500 km s−1 in the Local Supercluster. We obtained surface photometry and determined structural parameters using sdss images. The rotational velocities and derived photometric parameters for most galaxies in small groups agree well with those corresponding to the three-parameter TFR. However, isolated galaxies appear to have systematically lower surface brightnesses and longer scale lengths for the same luminosity than galaxies in small groups. This may indicate on average twice larger Hi-to-optical disk size ratios for our sample of isolated dIrrs, because their Hi surface densities calculated using the optical diameters look normal.