We present a numerical study of the high-quality modes in two-dimensional dielectric stadium microcavities. Although the classical ray mechanics is fully chaotic in a stadium billiard, all of the high-quality modes show a ``strong scar'' around unstable periodic orbits. when the deformation (ratio of the length of the straight segments over the diameter of the half circles) is small, the high-quality modes correspond to whispering-gallery-type trajectories and their quality factors decrease monotonically with increasing deformation. At large deformation, each high-quality mode is associated with multiple unstable periodic orbits. Its quality factor changes nonmonotonically with the deformation, and there exists an optimal deformation for each mode at which its quality factor reaches a local maximum. This unusual behavior is attributed to the interference of waves propagating along different constituent orbits that could minimize light leakage out of the cavity.