This study presents an efficient algorithm for computing precisely the Hankel singular values of linear singularly perturbed systems. The algorithm is obtained in terms of reduced-order problems and avoids numerical ill-conditioning associated with singularly perturbed systems when the singular perturbation parameter is very small. The study compares the presented algorithm with the algorithm that exists in the control engineering literature and demonstrates its superiority. In addition, an analysis of system order reduction via balancing and singular perturbations is performed and it is concluded that the system order reduction via balancing is more general than the system order reduction obtained via the method of singular perturbations.