  In our recent works, a new approach for constructing tree amplitudes, based
on exploiting soft behaviors, was proposed. In this paper, we extend this
approach to effective theories for gluons which incorporate higher-derivative
interactions. By applying our method, we construct tree Yang-Mills (YM) and
Yang-Mills-scalar (YMS) amplitudes with the single insertion of $F^3$ local
operator, as well as the YM amplitudes those receive contributions from both
$F^3$ and $F^4$ operators. All results are represented as universal expansions
to appropriate basis. We also conjecture a compact general formula for tree YM
amplitudes with higher mass dimension, which allows us to generate them from
ordinary YM amplitudes, and discuss the consistent factorizations of the
conjectured formula.
