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Understanding the properties of dust produced during the asymptotic giant branch phase of stellar evolution is important for understanding the evolution of stars and galaxies. Recent observations of the carbon AGB star R Scl have shown that observations at far-infrared and submillimetre wavelengths can effectively constrain the grain sizes in the shell, while the total mass depends on the structure of the grains (solid vs. hollow or fluffy). We aim to constrain the properties of the dust observed in the submillimetre in the detached shells around the three carbon AGB stars U Ant, DR Ser, and V644 Sco, and to investigate the constraints on the dust masses and grain sizes provided by far-infrared and submm observations. We observed the carbon AGB stars U Ant, DR Ser, and V644 Sco at 870 micron using LABOCA on APEX. Combined with observations from the optical to far-infrared, we produced dust radiative transfer models of the spectral energy distributions (SEDs) with contributions from the stars, present-day mass-loss and detached shells. We tested the effect of different total dust masses and grain sizes on the SED, and attempted to consistently reproduce the SEDs from the optical to the submm. We derive dust masses in the shells of a few 10e-5 Msun, assuming spherical, solid grains. The best-fit grain radii are comparatively large, and indicate the presence of grains between 0.1 micron-2 micron. The LABOCA observations suffer from contamination from 12CO(3-2), and hence gives fluxes that are higher than the predicted dust emission at submm wavelengths. We investigate the effect on the best-fitting models by assuming different degrees of contamination and show that far-infrared and submillimetre observations are important to constrain the dust mass and grain sizes in the shells., Comment: Accepted by A&A