We show that the phase diagram of the (001) Pb Mg1 3 Nb2 3 O3 -x PbTiO3 (PMN- x PT) (x=0.00, 0.06, 0.13, and 0.24) and (111) PMN-0.24PT lead-magnesium niobate mixed with lead titanate possesses a quasivertical line in the E electric field - T temperature plot, which hardly depends on the field. The existence of this line has been confirmed by independent studies of single crystals grown in different laboratories, by measuring the dielectric permittivity, compliances, and optical transmission, also in different laboratories. A thermal hysteresis inherent to first order phase transitions complicates the phase diagram. The piezoelectric coefficients of the (001) PMN- x PT (x = 0.06 and 0.13) have two peaks versus temperature, at finite fields. The first peak is due to the quasivertical phase boundary. The second is in the vicinity of a turning point of the Tm (E) temperature of the dielectric permittivity diffuse maximum. We show that the second peak prevails at reasonable fields, and the piezoelectric coefficients have comparatively large values at this peak, even at small x. © 2007 The American Physical Society.