Strain-free GaAs quantum dots (QDs) are fabricated by filling droplet-etched nanoholes in AlGaAs. Using a template of nominally identical nanoholes, the QD size is precisely controlled by the thickness of the GaAs filling layer. Atomic force microscopy indicates that the QDs have a cone-shell shape. From single-dot photoluminescence measurements, values of the exciton emission energy (1.58..1.82 eV), the exciton–biexciton splitting (1.8..2.5 meV), the exciton radiative lifetime of bright (0.37..0.58 ns) and dark (3.2..6.7 ns) states, the quantum efficiency (0.89..0.92), and the oscillator strength (11.2..17.1) are determined as a function of the dot size. The experimental data are interpreted by comparison with an atomistic model.