XML is becoming widely used as a standard data format on the Web. Unlike SGML, XML documents do not require having their schemas. Since design of schemas of XML documents is not an easy task, a significant number of XML documents will be simply well-formed. We focus on miscellaneous well-formed XML documents with no common schemas. We articulate issues related to query processing of those well-formed XML documents using standard data formats or vocabularies as namespaces. We believe that an end-user's typical queries against XML databases will be very terse as found in current HTML searching engines. However, unlike HTML search engines, XML database systems should return appropriate XML subdocuments as a granule of query results. The authors formulate a class of queries, which is a counterpart of a simple class of queries in current HTML search engines. Then, we define a new function which serves as a basis for identifying appropriate XML subdocuments as results of such queries and we introduce indices in order to process such queries efficiently.