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Multitouch displays represent a promising technology for the display and manipulation of data. While the manipulation of 2D data has been widely explored, 3D manipulation with multitouch displays remains largely unexplored. Based on an analysis of the integration and separation of degrees of freedom, we propose a taxonomy for 3D manipulation techniques with multitouch displays. Using that taxonomy, we introduce Depth-Separated Screen-Space (DS3), a new 3D manipulation technique based on the separation of translation and rotation. In a controlled experiment, we compared DS3 with Sticky Tools and Screen-Space. Results show that separating the control of translation and rotation significantly affects performance for 3D manipulation, with DS3 performing faster than the two other techniques.