Applying spectral dynamics methods to one typical N-body model with a barlens, we dissect the modelled bar into separate components supported by completely different types of orbits. We identify at least four components: a narrow elongated bar, a boxy bar, and two components contributing to the barlens. We analyse the vertical structure of all components that make up the thick part of the bar, which has a boxy/peanut shape (B/P bulge). We show that the 'peanut' shape is mainly due to the orbits that assemble the boxy part of the face-on bar. We associate the X-shape with the narrow and elongated bar. The wider part of the barlens with square-like isophotes contributes to the boxy shape of the B/P bulge when we observe the galaxy edge-on. However, the part of the barlens with rounded isophotes in the face-on view is a rather flat structure in the vertical direction without any significant off-centre protrusions. Thus, for the first time, we demonstrate that the rounded face-on barlens cannot be entirely associated with the B/P bulge.