The usual assumption in direct dark matter searches is to consider only the spin-dependent or spin-independent scattering of dark matter particles. However, especially in models with light dark matter particles O(GeV/c^{2}), operators which carry additional powers of the momentum transfer q^{2} can become dominant. One such model based on asymmetric dark matter has been invoked to overcome discrepancies in helioseismology and an indication was found for a particle with a preferred mass of 3 GeV/c^{2} and a cross section of 10^{-37} cm^{2}. Recent data from the CRESST-II experiment, which uses cryogenic detectors based on CaWO_{4} to search for nuclear recoils induced by dark matter particles, are used to constrain these momentum-dependent models. The low energy threshold of 307 eV for nuclear recoils of the detector used, allows us to rule out the proposed best fit value above.
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