  The standard picture of viable higher-dimensional theories is that extra
dimensions manifest themselves at short distances only, their effects being
negligible at scales larger than some critical value. We show that this is not
necessarily true in models with infinite extra dimensions. As an example, we
consider a five-dimensional scenario with three 3-branes in which gravity is
five-dimensional both at short {\it and} very long distance scales, with
conventional four-dimensional gravity operating at intermediate length scales.
A phenomenologically acceptable range of validity of four-dimensional gravity
extending from microscopic to cosmological scales is obtained without strong
fine-tuning of parameters.
