The multitouch functionality of tabletop computers is often augmented by the use of tangible objects that offer an intuitive and haptic alternative to interaction and manipulation. However, employing tangibles can also lead to less desirable effects, such as occlusion or lack of precision. In this paper we highlight the design and implementation of ring-like tangible objects: TangibleRings. They do not occlude the objects underneath them and also support the detection of touch events inside their perimeter. Additionally, multiple rings may be nested within one another in order to combine ring functionalities or produce more complex filters.