  We investigate the origin of order in the low-lying spectra of many-body
systems with random two-body interactions. Our study based both on analytical
as well as on numerical arguments shows that except for the most $J$-stretched
states, the ground states in the higher $J$-sectors are more orderly and
develop larger energy gaps than the ones in the J=0-sector. Due to different
characteristic energy scales in different $J$-sectors the J=0 ground states may
predominate only when all the states are taken together.
