Navigation in multi-scale virtual environments (MSVE) requires the adjustment of the navigation parameters to ensure optimal navigation experiences at each level of scale. In particular, in immersive stereoscopic systems, e.g. when performing zoom-in and zoom-out operations, the navigation speed and the stereoscopic rendering parameters have to be adjusted accordingly. Although this adjustment can be done manually by the user, it can be complex, tedious and strongly depends on the virtual environment. In this work we propose a new multi-scale navigation technique named GiAnt (GIant/ANT) which automatically and seamlessly adjusts the navigation speed and the scale factor of the virtual environment based on the user's perceived navigation speed. The adjustment ensures an almost-constant perceived navigation speed while avoiding diplopia effects or diminished depth perception due to improper stereoscopic rendering configurations. The results from the conducted user evaluation shows that GiAnt is an efficient multi-scale navigation which minimizes the changes of the scale factor of the virtual environment compared to state-of-the-art multi-scale navigation techniques.