  We investigate the origin of order in the low-lying spectra of many-body
systems with random two-body interactions. Contrary to the common belief our
study based both on analytical as well as on numerical arguments shows that
these are the higher $J$-sectors whose ground states are more orderly than the
ones in the J=0-sector. A predominance of J=0 ground states turns out to be the
result of putting on together states with different characteristic energy
scales from different $J$-sectors.
