  We study how theories defined in (extra-dimensional) spaces with localized
defects can be described perturbatively by effective field theories in which
the width of the defects vanishes. These effective theories must incorporate a
``classical'' renormalization, and we propose a renormalization prescription a
la dimensional regularization for codimension 1, which can be easily used in
phenomenological applications. As a check of the validity of this setting, we
compare some general predictions of the renormalized effective theory with
those obtained in a particular ultraviolet completion based on deconstruction.
