The validity of the unitarised Born (B II) approximation for representing the T-matrix elements for electron-polar-molecular collisions is investigated for a number of polar systems. For intermediate and high values of the angular momentum (usually l>or approximately=5), the B II results are in excellent agreement with those of a more elaborate close-coupling calculation. The method provides an efficient, economical means for calculating the higher angular momenta T-matrix elements that are needed in the completion formulae for polar-molecular cross sections. The methods have an advantage over such comparable schemes as the fixed-point-dipole technique in that contributions from potential moments above the dipole can be simply included.