The wave-based computational method named Variational Theory of Complex Rays (VTCR) is revisited in order to improve its robustness and its efficiency to solve transient dynamic problems including medium frequencies. The first problem addressed in the paper concerns the ill-conditioning of wave-based computational approaches. We introduce the concept of “effective portrait” which provides a new framework to the VTCR with a strong reduction of the conditioning number. The second issue deal with the computation over a large frequency bandwidth for wich the Proper Generalised Decomposition (PGD) has been retained. A thorough analysis of the efficiency and the limitations of the PGD-VTCR is given. The last issue concerns the synergy between the PGD-VTCR and the exponential window method for solving transient problems.