  We study soft wall models that can embed the Standard Model and a naturally
light dilaton. Exploiting the full capabilities of these models we identify the
parameter space that allows to pass Electroweak Precision Tests with a moderate
Kaluza-Klein scale, around $2$ TeV. We analyze the coupling of the dilaton with
Standard Model (SM) fields in the bulk, and discuss two applications: i) Models
with a light dilaton as the first particle beyond the SM pass quite easily all
observational tests even with a dilaton lighter than the Higgs. However the
possibility of a 125 GeV dilaton as a Higgs impostor is essentially disfavored;
ii) We show how to extend the soft wall models to realize a 750 GeV dilaton
that could explain the recently reported diphoton excess at the LHC.
