We study the problem of update propagation across views in the setting where both the view and the source database are XML documents. We consider a simple class of XML views that remove selected parts of the source document. The considered update operations permit to insert and delete subtrees of the document. We focus on constructing propagations that are 1) schema compliant i.e., when applied to the source document they give a document that satisfies the document schema; 2) side-effect free i.e., the view of the new source document is exactly as the result of applying the user update to the old view. We present a special structure allowing to capture all such propagations. We also show how to use this structure to capture only those propagations that affect minimally the parts of the document which are not visible in the view. Finally, we present a general outline of a polynomial algorithm constructing a unique propagation.