We present a comparative study, down to the single-molecule level, of the linewidth and multiplet structure of the optical transitions of 2.3,8.9-dibenzanthanthrene (DBATT) in shock-frozen solutions of n-decane, n-undecane, and n-tetradecane. The n-alkane matrices show weak structural ordering and distinct incorporations of the DBATT molecules have been recognized. The order does not increase, nor does the ensemble optical linewidth decrease going from bulk to sub-volumes of less than 1 mum(3). The relation between lateral position, orientation of the transition moment, and transition frequency has been investigated using single-molecule fluorescence-excitation and polarization spectroscopy. The distribution of the orientation is found not to depend on frequency and vice versa. Structural ordering on a microscopic scale is found not to be decisive as regards the linewidth and multiplet structure.