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We report three newly discovered exoplanets from the SuperWASP survey. WASP-127b is a heavily inflated super-Neptune of mass 0.18 +/- 0.02 M_J and radius 1.37 +/- 0.04 R_J. This is one of the least massive planets discovered by the WASP project. It orbits a bright host star (Vmag = 10.16) of spectral type G5 with a period of 4.17 days. WASP-127b is a low-density planet that has an extended atmosphere with a scale height of 2500 +/- 400 km, making it an ideal candidate for transmission spectroscopy. WASP-136b and WASP-138b are both hot Jupiters with mass and radii of 1.51 +/- 0.08 M_J and 1.38 +/- 0.16 R_J, and 1.22 +/- 0.08 M_J and 1.09 +/- 0.05 R_J, respectively. WASP-136b is in a 5.22-day orbit around an F9 subgiant star with a mass of 1.41 +/- 0.07 M_sun and a radius of 2.21 +/- 0.22 R_sun. The discovery of WASP-136b could help constrain the characteristics of the giant planet population around evolved stars. WASP-138b orbits an F7 star with a period of 3.63 days. Its radius agrees with theoretical values from standard models, suggesting the presence of a heavy element core with a mass of ~10 M_earth. The discovery of these new planets helps in exploring the diverse compositional range of short-period planets, and will aid our understanding of the physical characteristics of both gas giants and low-density planets.