: Over the recent years, very little effort has been made to give XPath a proper algebraic treatment. The only laudable exception is the Natix Algebra (NAL) which defines the translation of XPath queries into algebraic expressions in a concise way, thereby enabling algebraic optimizations. However, NAL does not capture various promising core XML query evaluation algorithms like, for example, the Holistic Twig Join. By integrating a logical structural join operator, we enable NAL to be compiled into a physical algebra, containing exactly those missing physical operators. We will provide several important query unnesting rules and demonstrate the effectivity of our approach by an implementation in the XML Transaction Coordinator (XTC)—our prototype of a native XML database system.