We present high-resolution 345-GHz interferometric observations of two extremely luminous (Lir≳ 1013 L⊙), submillimetre-selected galaxies (SMGs) in the Cosmic Evolution Survey (COSMOS) field with the Submillimeter Array (SMA). Both targets were previously detected as unresolved point sources by the SMA in its compact configuration, also at 345 GHz. These new data, which provide a factor of ≳3 improvement in resolution, allow us to measure the physical scale of the far-infrared in the submillimetre directly. The visibility functions of both targets show significant evidence for structure on ∼0.5–1-arcsec scales, which at z≳ 1.5 translates into a physical scale of ∼5–8 kpc. Our results are consistent with the angular and physical scales of two comparably luminous objects with high-resolution SMA follow-up, as well as radio continuum and CO sizes of other SMGs. These relatively compact sizes (≲5–10 kpc) argue strongly for merger-driven starbursts, rather than extended gas-rich discs, as the preferred channel for forming SMGs.