CRESST is a direct dark matter search experiment, aiming for an observation of nuclear recoils induced by the interaction of dark matter particles with cryogenic scintillating calcium tungstate crystals. Instead of confining ourselves to standard spin-independent and spin-dependent searches, we re-analyze data from CRESST-II using a more general effective field theory (EFT) framework. On many of the EFT coupling constants, improved exclusion limits in the low-mass region (< 3-4 GeV) are presented.