Electrical properties of molecules are difficult to compute accurately, and traditional calculations typically require large basis sets with multiple sets of diffuse and polarization functions. Ditchfield, Sadlej, and Almlof have shown that much smaller basis sets can be used if electric dependence is incorporated into the basis set. We have combined the features of these methods and allowed the center of each Gaussian, A, to depend on the field, epsilon, according to A(epsilon) = A(0) - alpha(n) lambda epsilon, where alpha is the Gaussian exponent, n is a fixed integer, and lambda is a parameter chosen to maximize the polarizability in a series of reference molecules. The field dependence is used in both the exponential and the preexponential factors in the Gaussian basis functions. Electric field dependent HF/6-31+G** calculations of dipole moments, polarizabilities, and infrared intensities are approximately the same quality as HF/6-311++G(3d,3p) calculations without field dependent functions (the improvement is most striking for the polarizabilities of linear molecules). Field dependence of the outer valence and diffuse functions appears to be the most important. The results for n = -2 and n = 0 are very similar; the existing codes for geometrical derivatives of the energy can be easily modified to compute improved electrical properties for the n = 0 case.