We have examined the compact structure in 250 flat-spectrum extragalactic radio sources using interferometric fringe visibilities obtained with the Very Long Baseline Array (VLBA) at 15 GHz. With projected baselines out to 440 Ml, we are able to investigate source structure on typical angular scales as small as 0.05 mas. This scale is similar to the resolution of the VLBI Space Observatory Programme data obtained on longer baselines at a lower frequency and with somewhat poorer accuracy. For 171 sources in our sample, more than half of the total flux density seen by the VLBA remains unresolved on the longest baselines. There are 163 sources in our list with a median correlated flux density at 15 GHz in excess of 0.5 Jy on the longest baselines; these will be useful as fringe finders for short-wavelength VLBA observations. The total flux densities recovered in the VLBA images at 15 GHz are generally close to the values measured around the same epoch at the same frequency with the RATAN-600 and University of Michigan Radio Astronomy Observatory telescopes.