Photoproduction of π0π0 and π0π± pairs from nuclei has been measured over a wide mass range (2H, 7Li, 12C, 40Ca, and natPb) for photon energies from threshold to 600 MeV. The experiments were performed at the MAMI accelerator in Mainz, using the Glasgow photon tagging spectrometer and a 4π electromagnetic calorimeter consisting of the Crystal Ball and TAPS detectors. A shift of the pion–pion invariant-mass spectra for heavy nuclei to small invariant masses has been observed for π0 pairs but also for the mixed-charge pairs. The precise results allow for the first time a model-independent analysis of the influence of pion final-state interactions. The corresponding effects are found to be large and must be carefully considered in the search for possible in-medium modifications of the σ-meson. Results from a transport model calculation reproduce the shape of the invariant-mass distributions for the mixed-charge pairs better than for the neutral pairs, but also for the latter differences between model results and experiment are not large, leaving not much room for σ-in-medium modification.