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We consider the Newton stratification on Iwahori double cosets for aconnected reductive group. We prove the existence of Newton strata whoseclosures cannot be expressed as a union of strata, and show how this is impliedby the existence of non-equidimensional affine Deligne-Lusztig varieties. Wealso give an explicit example for a group of type $A_4$.

Closure relations of Newton strata in Iwahori double cosets