We examine the consistency of light dark matter (DM) elastic scattering in CoGeNT, DAMA, and CDMS-Silicon in light of constraints from XENON, CDMS, LUX, PICASSO and COUPP. We consider a variety of operators that have been employed to reconcile anomalies with constraints, including anapole, magnetic dipole, momentum-dependent, and isospin-violating DM. We find that elastic scattering through these alternative operators does not substantially reduce the tension between the signals and the null constraints for operators where at least two of the three purported signals map onto a common space in the DM mass--scattering cross-section plane. Taking a choice of the scintillation efficiency that lies at the $-1 σ$ region of the Manzur et al measurement relieves tension between signals and the LUX constraint---in particular for a magnetic dipole interaction and a xenophobic interaction (though for the latter the signal regions do not substantially overlap). We also find that modest changes in the halo model does not alter this result. We conclude that, even relaxing the assumption about the type of elastic scattering interaction and taking a conservative choice for the scintillation efficiency, LUX and the results from other null experiments remain in tension with a light DM elastic scattering explanation of direct detection anomalies. ; Comment: 27 pages, 8 figures; v2: typos corrected, a few references added, and in the appendix: discussion of LUX analysis expanded and clarifications made on XENON100 analysis