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We report the discovery by the WASP transit survey of two new highly irradiated giant planets. WASP-64 b is slightly more massive (1.271 ± 0.068 MJup) and larger (1.271 ± 0.039 RJup) than Jupiter, and is in very-short (a = 0.02648 ± 0.00024 AU, P = 1.5732918 ± 0.0000015 days) circular orbit around a V = 12.3 G7-type dwarf (1.004 ± 0.028 M⊙, 1.058 ± 0.025 R⊙, Teff = 5500 ± 150 K). Its size is typical of hot Jupiters with similar masses. WASP-72 b has also a mass a bit higher than Jupiter’s (1.461-0.056+0.059 MJup) and orbits very close (0.03708 ± 0.00050 AU, P = 2.2167421 ± 0.0000081 days) to a bright (V = 9.6) and moderately evolved F7-type star (1.386 ± 0.055 M⊙, 1.98 ± 0.24 R⊙, Teff = 6250 ± 100 K). Despite its extreme irradiation (~5.5 × 109 erg s-1 cm-2), WASP-72 b has a moderate size (1.27 ± 0.20 RJup) that could suggest a significant enrichment in heavy elements. Nevertheless, the errors on its physical parameters are still too high to draw any strong inference on its internal structure or its possible peculiarity.