We elaborate on the idea that five-dimensional models where sequestering is spoiled due to contact interactions induced by vector multiplets may still be mildly sequestered if a global version of the gauge symmetry associated to the latter survives in the hidden sector. Interestingly, it has been argued that although in such a situation non-trivial current current contact interactions are induced by the heavy vector modes, these do not induce soft scalar masses, as a consequence of the global symmetry. We perform a detailed study of how this hybrid mechanism can be implemented in supergravity and string models, focusing on the prototypical case of heterotic M-theory orbifolds. We emphasize that in general the mechanism works only up to subleading effects suppressed by the ratio between the global symmetry breaking scale in the hidden sector and the vector mass scale or the Planck scale. We also argue that this mild sequestering mechanism allows to rehabilitate the scenario of dilaton domination of supersymmetry breaking, which is incompatible with dilaton stabilization in its original version, by exploiting the fact that hidden brane fields do contribute to the cosmological constant but not to soft terms, thanks to the global symmetry. (C) 2010 Elsevier B.V. All rights reserved.