Using the 3.′2 Arecibo beam, we have mapped the HI envelopes of a sample of 70 irregular galaxies (Sdm, Sm, Im and BCD), including 45 from the Virgo Cluster Catalog, 14 Field galaxies at similar redshifts, and 11 Nearby dwarfs chosen to give a complete sample out to 6 Mpc, within the Arecibo declination range. To explore correlations among variables characterizing the size and dynamics of these galaxies, we have combined this sample with all other mappings (multiple single beams and synthesis array) of irregulars and of spiral galaxies spanning the same redshift range (out to about 20 Mpc) available in the literature. In all, there are 128 mapped dwarfs and 119 mapped spirals in this dataset. We obtain the following correlations: rH,max = (2.75 ± .15)r25(0.890±.034) where both HI and optical radii are in kpc; LB = (3.59±.80) × 106rgm(2.70±.11) where LB is in solar luminosities and rgm is the geometric mean of rH,max and r25; LB = (125±36) Vc(3.62±.19) where the rotation speed is in km s−1; MH = (9.3 ± 1.1) × 106rgm(1.977±.056) where the HI mass is in solar units; and LB = (1.9+2.7−1.1) × 10−3Mndyn(1.164±.043) where Mdyn = Vc2rgm/G.