Angular correlations in the reaction plane for the 16.62- and 16.92-MeV, Jπ=2+ states in Be8 have been measured for the reaction Li6(Li6,α1)Be8*-->2α at a bombaarding energy of 5.5 MeV with α1 detected at 15° in the lab. The correlations for the two states are identical to a multiplicative factor at all decay alpha angles. Another alpha-alpha coincidence run at 5.0-MeV bombarding energy was performed to measure the ratio of intensities of these two states. The same data show a peak which may represent a 19.9-MeV Be8 state with a width of 1.3 MeV. In addition, measurements of the ratio of the differential cross sections of the 16.62- and 16.92-MeV levels over a range of bombarding energies from 4.3 to 5.5 MeV indicate that the relative intensity of the 16.62-MeV level to that of the 16.92-MeV level is a constant equal to 1.22+/-0.08. These results favor a description of these states as strongly mixed in isobaric spin.