We present an X-ray scattering study of the effect of mixed chain lengths on the plastic-crystalline rotator phases of n-alkanes. When the width of the distribution is large, as is the case of commercial waxes and other alkane-like systems such as lipids, the range of stability of the rotator phases is increased, making the rotator phases occupy a more significant portion of the phase diagram than in pure model materials. As the distribution is widened several universal trends are found : the distortion in the orthorhombic R(I) phase is reduced, the hexagonal R(II) rotator phase is favored over the distorted R(I) phase, and the tilted R(V) phase is suppressed. These effects can be understood in terms of a weakened coupling between layers caused by the spread in chain lengths.