  A measurement of the Higgs trilinear self coupling $\lambda_{hhh}$ will test
the Standard Model Higgs potential. But can it reveal information that cannot
be learned otherwise? By analyzing several simple extensions of the Standard
Model scalar sector we show that this measurement might give a first hint for
New Physics modifying the electroweak symmetry breaking. Combining the
measurements of $\lambda_{hhh}$ and $\lambda_{hVV}$ ($V=W,Z$) is particularly
powerful in distinguishing between various models of New Physics and in
providing unique information on these models.
