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Past studies of dispersion with float-pairs have indicated that they may remain close together for much longer when they equilibrate on the same isopycnal, presumably due to the reduced influence of vertical shear. To examine this question more closely, we use a set of 13 and 15 float pair combinations that equilibrated within 0.1°C (∼σ_θ=0.01 kg m^-3) of each other on two density surfaces in the main thermocline in a Lagrangian dispersion study. Their average rate of separation after launch was 0.0021±0.0014 ms^-1 (∼5.5 km after 30 days). Relative dispersion is accurately expressed by 2>=4•10⁶ exp(t/10.8) m² from start to about 30 days. Relative diffusivity (K) versus separation dropped well below the classical 4/3rds power law settling out at about 2-3 m²s^-1 for separations less than ∼6 km, far lower than results from other float studies, but in accord with dye dispersion estimates.