Three-dimensional dislocation dynamics simulations were employed to examine how hard coatings affect plastic deformation in micron- and submicron-sized, single-crystal pillars ("micropillars") of nickel. Cross-slip of dislocations in the coated samples was found to be necessary for the formation of banded structures and subcells. Our simulations thus offer an explanation for both the significant increases in compressive strength and the higher strain-hardening rate as well as formation of banded structures in coated micropillars.