The recently proposed single Lanczos propagation method [J. Chem. Phys. 111, 9944 (1999)] for calculating multiple transition amplitudes is made more efficient in several aspects. It is shown that the amplitudes can be calculated without the explicit calculation and storage of the Lanczos eigenvectors, thus significantly reducing the computational costs, particularly for long propagation. It is also shown that symmetry adaptation can be implemented in the Lanczos propagation in a straightforward manner. In particular, eigenspectra in multiple irreducible representations can be determined from a single recursion by projecting the symmetrized Lanczos states at each step. The accuracy and efficiency of the improved methods are ascertained by numerical tests of realistic triatomic and tetratomic systems. (C) 2001 American Institute of Physics.