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A subclass C·0(C0(P ), fin) of the class of C·0-contractions is introduced and studied. This subclass is a generalization of the subclass of C·0-contractions with finite defect indices, and it includes the C·0-contractions T for which dim Ker T ∗ <∞ and the defect operator (I − T ∗T )1/2 belongs to the Hilbert–Schmidt class. For an operator of class C·0(C0(P ), fin), a Jordan model is constructed, and it is proved that the lattices of invariant subspaces remain isomorphic under the quasiaffine transfor-

$C\_\{\textperiodcentered 0\}$-contractions: a Jordan model and lattices of invariant subspaces