Suppose that we are able to compute for each induced subhypergraph a coloring in c₁ colors having discrepancy at most D. Then there are colorings in arbitrary numbers c₂ of colors having discrepancy at most 11/10 c ₁ ² D. A c₂-coloring having discrepancy at most 11/10 c ₁ ² D+3c₁ ^-k ∣X∣ can be computed from (c₁-1)(c₂-1)k colorings in c₁ colors having discrepancy at most D with respect to a suitable subhypergraph of H. A central step in the proof is to show that a fairly general rounding problem (linear discrepancy problem in c₂ colors) can be solved by computing low-discrepancy c₁-colorings.