System and methods are disclosed to selectively project individual UI elements of display images from stereoscopic HMDs as monocular or stereoscopic images. An UI element may be tagged for rendering as a monocular image or as stereoscopic images with a stereo separation to create a perception of depth. Tagging of UI elements as monocular images or stereoscopic images may be based on whether the UI elements are persistent elements. Persistent elements present information to the user but do not require the user's focused attention. Persistent elements may be rendered as monocular images to allow the user to focus on other UI elements or on the real world while maintaining awareness of information presented by the persistent elements. In contrast, non-persistent UI elements may require the user's focused attention. Non-persistent UI elements may be rendered as stereoscopic images for projection at a specific depth plane to invite the user's focus.