Bivariate dependence may be of such complexity that no single family of known parametric copulas is able to give an acceptable goodnes of fit. The gluing copula approach may be of good help in decomposing a complex non monotone dependence into easier to model piecewise monotone dependencies. This is good news for the vine copula approach since bivariate copulas are building blocks of such approach in higher dimensions. An application to real data in economics and geophysics will be discussed.