  We present a method to derive conservative upper limits on the coupling
constants of the effective theory of dark matter-nucleon interactions, taking
into account the interference among operators. The method can be applied in any
basis, and can be easily particularized to any UV complete model. To illustrate
our method, we use the IceCube constraints on an exotic neutrino flux from dark
matter annihilations in the Sun to derive conservative upper limits on the dark
matter-nucleon coupling constants of the effective theory, as well as to derive
conservative upper limits on the dark matter-proton and dark matter-neutron
scattering cross-sections.
