In Tore Supra, density fluctuations near to the plasma edge present up-down asymmetries which increase with the edge safety factor, weakly depend on density and reverse with the plasma current direction. The strongest asymmetries are observed in the particular case where the plasma is leaning on the lower limiter close to the measurement chord, with a connection length along the magnetic field line to the lower measurement region of the order of 0.6 m. For strong asymmetries, top and bottom k-spectra have different slopes. Possible theoretical explanations for these asymmetries are briefly discussed.