  Dark matter (DM) direct detections are investigated for models with the
following properties: isospin-violating couplings, exothermic scatterings,
and/or a light mediator, with the aim to reduce the tension between the CDMS-Si
positive signals and other negative searches. In particular, we focus on the
non-standard effective operators which could lead to the spin-independent
DM-nucleus scatterings with non-trivial dependences on the transfer momentum or
DM velocity. As a result, such effective operator choices have the very mild
effects on the final fittings. Furthermore, by including the latest constraints
from LUX, PandaX-II, XENON1T and PICO-60, we find that, for almost all the
considered models, the predicted CDMS-Si signal regions are either severely
constrained or completely excluded by the LUX, PandaX-II, XENON1T and PICO-60
data, including the most promising Xe-phobic exothermic DM models with/without
a light mediator. Therefore, we conclude that it is very difficult for the
present DM framework to explain the CDMS-Si excess.
