We present updated constraints on dark matter models with momentum-dependent or velocity-dependent interactions with nuclei, based on direct detection and solar physics. We improve our previous treatment of energy transport in the solar interior by dark matter scattering, leading to significant changes in fits to many observables. Based on solar physics alone, DM with a spin-independent $q^{4}$ coupling provides the best fit to data, and a statistically satisfactory solution to the solar abundance problem. Once direct detection limits are accounted for however, the best solution is spin-dependent $v^2$ scattering with a reference cross-section of 10$^{-35}$ cm$^2$ (at a reference velocity of $v_0=220$ km s$^{-1}$), and a dark matter mass of about 5 GeV.
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