We　study　a　number　of　statistical　phrase-based　translation　models　that　are　constrained　by　adjacent　reordering.　Under　this　constraint,　we　derive　polynomial　decoding　algorithms　respectively　for　basic　and　Koehn＇s　phrase-based　models,　with　an　implication　that　many　statistical　phrase-based　models　may　also　be　decodable　in　polynomial　time.　Using　NIST　as　a　metric,　we　show　that　the　presented　decoding　algorithms　can　achieve　a　relative　improvement　of　about　2.7%　over　Pharaoh　under　the　same　experimental　conditions.　©2010　IEEE.