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Kirillov-Reshetikhin modules are a family of modules over quantum affine algebras. In this talk, we consider K-R modules over algebras of type $D_n^{(1)}$ associated with an integer multiple of the second fundamental weight. Combinatorially, this means that the vertices of the crystal graph of the module are indexed by rectangular tableaux with two rows. We will first specify what constitutes a legal tableau in this context, and then describe the action of the quantum affine algebra on the associated module elements. Finally, we will see some facts which strongly suggest that these crystals are perfect.