  We discuss the impact and potential discovery of physics beyond the Standard
Model, coupling to the Higgs sector, at the LHC. Using a model-independent
effective Lagrangian approach, pure Higgs and Higgs-gauge operators are
analyzed, and their origin in terms of tree-level exchange of unknown heavy
messengers is systematically derived. It is demonstrated that early signals at
the LHC may result from a simultaneous modification of Higgs-fermion and
Higgs-gauge boson couplings induced by those operators, pointing towards
singlet scalar or a triplet vector -- barring fine-tuned options. Of course,
the Higgs discovery itself will also be affected by such new couplings. With
increasing statistics, the remaining options can be discriminated from each
other. On the other hand, the discovery of a new scalar doublet may require
technology beyond the LHC, since the Higgs self-couplings have to be measured.
  Our conclusions are based on the complete set of tree-level decompositions of
the effective operators unbiased by a specific model.
