This paper deals with map-based self-localization in a dynamic environment. In order to detect localization features, laser rangefinders traditionally scan a plane: we hypothesize the existence of a “low frequency cross-section” of the 3D environment (informally, over people heads), where even highly dynamic environments become more “static” and “regular”. We show that, by accurately choosing the laser scanning plane, problems related to moving objects, occluded features, etc. are simplified. Experimental results showing hours of continuous work in a real-world, crowded scenario, with an accuracy of about 2.5cm and a speed of 0.6m/sec, demonstrate the feasibility of the approach.