  We study the Laplacian in deformed thin (bounded or unbounded) tubes in
?$\R^3$, i.e., tubular regions along a curve $r(s)$ whose cross sections are
multiplied by an appropriate deformation function $h(s)> 0$. One the main
requirements on $h(s)$ is that it has a single point of global maximum. We find
the asymptotic behaviors of the eigenvalues and weakly effective operators as
the diameters of the tubes tend to zero. It is shown that such behaviors are
not influenced by some geometric features of the tube, such as curvature,
torsion and twisting, and so a huge amount of different deformed tubes are
asymptotically described by the same weakly effective operator.
