Levels at 6.69, 6.88, and 6.89 MeV were observed in the 16O(16O, α)28Si reaction, and angular correlations were measured for the resulting gamma-ray transitions, using the geometry in which the alpha particle is detected at 0°. The level at 6.69 MeV had not been reported previously and was assigned spin and parity 0+. The doublet of levels at 6.88–6.89 MeV was not resolved in these measurements, but angular correlations of the gamma-ray transitions were possible, using spectrum subtraction techniques. One member of the doublet, previously assigned spin 3, has a strong ground-state transition; the angular correlation for this transition confirms a 3− assignment to this level. The other member of the doublet, which decays almost entirely to the first excited state, could not be assigned a spin on the basis of these measurements. However, taken in conjunction with other measurements, an assignment of 4+ is favored.