Within a broad class of inflationary models we critically analyze the way initial quantum fluctuations on a new-physics hypersurface (NPH) affect standard predictions for large-scale cosmological perturbations. We find that these so-called transplanckian effects depend crucially on the definition of the "vacuum state" in particular on which Hamiltonian is minimized on the NPH in order to select such a state. Transplanckian effects can be made much smaller than previously suggested if sufficiently "adiabatic" Hamiltonians are minimized.