In this paper we first present several alternative techniques for system order reduction based on system balancing by employing the method of singular perturbations. The techniques obtained have the same robustness accuracy evaluated with respect to the H-infinity norm of the reduced-order system as the two techniques existing in the control literature known as the direct truncation and balancing residualization methods. The newly proposed techniques preserve the exact DC gain as the original system, and produce very good to excellent accuracy at low and medium frequencies. We also present a simple formula that fixes the DC gain for the direct truncation method. In the second part of the paper we propose how to perform order-reduction of a balanced system using theory of singular perturbations that can produce very good accuracy at high frequencies, particularly for systems that have lightly damped highly oscillatory modes. The result obtained for such kind of systems requires that the modes with higher Hankel singular values should be neglected and those with smaller Hankel singular values should be retained. This is a counter-intuitive result in the spirit of H-infinity theory, but an intuitive result in the spirit of theory of singular perturbations. The second part of the paper raises an important question about validity of the system robustness estimate based on the H-infinity norm for linear systems with lightly damped highly oscillatory modes.