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We conjecture that the massless gauge theory of Yang-Mills deformed by a higher-derivative Tr(F^3) operator will not be tree-level color-dual without an infinite number of additional counterterms. The requirement of color-dual kinematics and consistent factorization between four- and five-points induces a tower of increasingly higher-dimensional operators. We find through explicit calculation that their amplitudes are consistent with the alpha' expansion of those generated by the (DF)^2+YM theory, a known color-dual theory where the Tr(F^2) term has been given a mass squared proportional to 1/alpha'. Considering consistent double-copy construction as a physical principle would suggest that a Tr(F^3)-based attempt at a color-dual resolution of the UV divergence of N=4 supergravity may be able to tame the bad ultraviolet behavior of the theory, but at the cost of field-theoretic locality.