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The distribution of the fine-structure splitting ħ δ 1 and of the biexciton binding energy ħ δ B are measured in a series of annealed InAs quantum dots. We find a decrease of ħ δ 1 from 96 μ eV to 6 μ eV with increasing annealing temperature, indicating a symmetrizing of the in-plane confinement potential. The biexciton binding energy shows only a weak dependence on the confinement energy, which we attribute to a compensation between decreasing confinement and decreasing separation of electron and hole.