  We present the constraints on the trilinear Higgs self coupling that arise
from loop effects in the $W$ boson mass and the effective sine predictions. We
compute the contributions to these precision observables of two-loop diagrams
featuring an anomalous trilinear Higgs self coupling. We explicitly show that
the same anomalous contributions are found if the analysis of $m_{
\scriptscriptstyle W}$ and $\mbox{$\sin^2 \theta^{{\rm lep}}_{{\rm eff}}$}$ is
performed in a theory in which the scalar potential in the Standard Model
Lagrangian is modified by an (in)finite tower of $(\Phi^\dagger \Phi)^n$ terms
with $\Phi$ the Higgs doublet. We find that the bounds on the trilinear Higgs
self coupling from precision observables are competitive with those coming from
Higgs pair production.
