As part of an astrometric program, we have used the Very Long Baseline Array to measure the trigonometric parallax of several young stars in the Taurus and Ophiuchus star-forming regions with great accuracy. Additionally, we have obtained an unprecedented sample of high-resolution (~ 1 mas) images of several young stellar systems. These images revealed that about 70% of the stars in our sample are very tight binary stars (with separations of a few mas). Since it is highly unlikely that 70% of all stars are such tight binaries, we argue that selection effects are at work.