  We present the results of a targeted search for intervening HI absorption in
six nearby, gas-rich galaxies using the Australia Telescope Compact Array
(ATCA). The sightlines searched have impact parameters of 10-20 kpc. By
targeting nearby galaxies we are also able to map their HI emission, allowing
us to directly relate the absorption-line detection rate to the extended HI
distribution. The continuum sightlines intersect the HI disk in four of the six
galaxies, but no intervening absorption was detected. Of these four galaxies,
we find that three of the non-detections are the result of the background
source being too faint. In the fourth case we find that the ratio of the spin
temperature to the covering factor ($T_{\mathrm{S}}/f$) must be much higher
than expected ($\gtrsim$5700 K) in order to explain the non-detection. We
discuss how the structure of the background continuum sources may have affected
the detection rate of HI absorption in our sample, and the possible
implications for future surveys. Future work including an expanded sample, and
VLBI observations, would allow us to better investigate the expected detection
rate, and influence of background source structure, on the results of future
surveys.
