With the discovery of high T c superconductivity (Tc: 7-8 K) in the organic conductor fl-(BEDT-TF)2I 3 under a soft pressure of 1.3 kbar, the pressure effect for 13, I2Br and IBr z salts is investigated to have a general aspect of the superconductivity. In the 13 salt, T c was originally 1.1-1.2 K at P = 0 kbar; above at least 1.3 kbar, T c suddenly increases up to 7-8 K and decreases smoothly to 1.2 K (7 kbar). The superconducting states were classified into "high T c state" and "low T c state" in the 13 salt. The high T c state remains after release of pressure. In the high T c state at 1.6 kbar, a tentative linear extrapolation of He2 to 0 K reaches 2 T (11 c*-axis) and 25 T (11 a-b plane) which is beyond the simple paramagnetic limit of 13T, while in the low T c state, 0.08T (11 c*-axis) and 2T (11 a-b plane). When the I3-anion is replaced by IBr z, the superconductivity is similar to the "high T c state" of the I 3 salt. In the I2Br salt, superconductivity is not observed down to 50 mK up to 3 kbar, which may be due to the disorder of the dipole moment of (Br-I-I) and (I-I-Br) in the crystal. Conductivity response against pressure at room temperature of the three salts is large and its magnitude is in order with the anion sizes.