  In an appendix to an earlier paper (cf. arXiv:1703.00984) we showed we showed
how to construct tunnels of positive scalar curvature and of arbitrarily small
length and volume connecting points in a \emph{three dimensional} manifold of
\emph{constant sectional curvature}. Here we generalize the construction to
arbitrary dimensions and require only positivity of the scalar curvature. This
version contains an added section on existence of arbitrarily narrow tunnels of
prescribed length.
