How can one learn as much as possible about masses/couplings of Dark Matter from LHC + Direct and Indirect Detection experiments?

There have recently been some interesting new results by Direct Detection experiments.
In particular, there is a new technology (COUPP) that uses a bubble chamber:
Improve Spin-Dpendent WIMP Limits from a Bubble Chamber
There is also the new
DAMA result

A review of the Direct Detection technologies from 2004 by Rick Gaitskell
Gaitskell Review
This also has some critiques of the DAMA results.

An interesting attempt to reconcile the DAMA/CDMS/Xe result is the inelastic DM approach of Weiner/Smith
Status of Inelastic DM (apparently this approach was valid post CRESST/ZEPPLIN, but no paper yet demonstrates it survies post-XENON--though I think one is in the works)

Are there models of particle physics that reconcile these experiments?
(How) would they appear at the LHC?

Another review relevant for collier physics:
Baltz, Battaglia, Peskin and Wizansky,