We present the results from two radio integrations at 8.4 GHz using the VLA . One of the fields , at 13 ^ { h } +43 ^ { \circ } ( SA13 field ) , has an rms noise level of 1.49 ~ { } \mu Jy and is the deepest radio image yet made . Thirty-four sources in a complete sample were detected above 7.5 ~ { } \mu Jy and 25 are optically identified to a limit of I=25.8 , using our deep HST and ground-based images . The radio sources are usually located within 0.5 ^ { \prime \prime } ( typically 5 kpc ) of a galaxy nucleus , and generally have a diameter less than 2.5 ^ { \prime \prime } . The second field at 17 ^ { h } +50 ^ { \circ } ( Hercules Field ) has an rms noise of 35 ~ { } \mu jy and contains 10 sources . We have also analyzed a complete flux density-limited sample at 8.4 GHz of 89 sources from five deep radio surveys , including the Hubble deep and flanking fields as well as the two new fields . Half of all the optical counterparts are with galaxies brighter than I=23 mag , but 20 % are fainter than I=25.5 mag . We confirm the tendency for the micro-Jansky radio sources to prefer multi-galaxy systems . The distribution of the radio spectral index between 1.4 and 8.4 GHz peaks at \alpha \approx - 0.75 ~ { } ( S \sim \nu ^ { + \alpha } ) , with a median value of -0.6 . The average spectral index becomes steeper ( lower values ) for sources below 35 ~ { } \mu Jy , and for sources identified with optical counterparts fainter than I=25.5 mag . This correlation may suggest that there is an increasing contribution from star-burst galaxies compared to active galactic nuclei ( AGNs ) at lower radio flux densities and fainter optical counterparts . The differential radio count between 7.5 and 1000 \mu Jy has a slope of -2.11 \pm 0.13 and a surface density of 0.64 sources ( arcmin ) ^ { -2 } with flux density greater than 7.5 ~ { } \mu Jy .