Query containment for conjunctive queries is the problem of checking whether a query q is contained in another query q′ with respect to a given Description Logic schema S. It is known that query containment can also be used to answer queries. Query containment is important in many areas, including information integration, query optimisation, and reasoning about Entity-Relationship diagrams, while query languages that allow the use of variables and individuals in a query, such as conjunctive queries, become a more and more important topic in the area of ontology development and the Semantic Web. We introduce the existing algorithms to decide query containment resp. query answering, and show by means of an example that these algorithms are incomplete for some cyclic queries. We highlight the sources of incompleteness that are easily overlooked in the development of suitable algorithms and suggest an extended algorithm to overcome these problems.