Interesting virtual environments that permit free exploration are rarely small. A number of techniques have been developed to allow people to walk in larger virtual spaces than permitted by physical extent of the virtual reality hardware, and in this paper we compare three such methods in terms of how they affect presence and spatial awareness. In our first psychophysical study, we compared two methods of reorientation and one method of redirected walking on subjects' presence and spatial memory while navigating a pre-specified path. We further compared the two reorientation methods in a second psychophysical study involving free exploration and navigation in a large virtual environment. Our results provide criteria by which the choice of a locomotion method for navigating large virtual environments may be selected.