The molecular orientation in monolayer J-aggregates of 3,3-di(gamma-sulfopropyl)5,5-dichlorotiamonomethinecyanine dye has been precisely estimated using improved linear polarization measurements in the fluorescence microscope in which a multiangle set of polarization data is obtained using sample rotation. The estimated molecular orientation supplemented with the previously established crystallographic constraints based on the analysis of the well-developed two-dimensional J-aggregate shapes unambiguously indicate the staircase type of molecular arrangement for striplike J-aggregates with the staircases oriented along strips. The molecular transition dipoles are inclined at an angle of similar to 25 degrees to the strip direction, whereas the characteristic strip vertex angle similar to 45 degrees is formed by the [100] and [110] directions of the monoclinic unit cell. Measurements of the geometry of partially unwound tubes and their polarization properties support the model of tube formation by close-packed helical winding of flexible monolayer strips. In the tubes, the long molecular axes are oriented at a small angle in the range of 5-15 degrees to the normal to the tube axis providing low bending energy. At a nanoscale, high-resolution atomic force microscopy imaging of J-aggregate monolayers reveals a complex quasi-one-dimensional organization.