  One of the strongest constraints on the existence of large, compact,
"gravity-only" dimensions comes from SN1987a. If the rate of energy loss into
these putative extra dimensions is too high, then the neutrino pulse from the
supernova will differ from that actually seen. The dominant mechanism for the
production of Kaluza-Klein gravitons and dilatons in the supernova is via
gravistrahlung and dilastrahlung from the nucleon-nucleon system. In this paper
we compute the rates for these processes in a model-independent way using
low-energy theorems which relate the emissivities to the measured
nucleon-nucleon cross section. This is possible because for soft gravitons and
dilatons the leading contribution to the energy-loss rate is from graphs in
which the gravitational radiation is produced from external nucleon legs.
Previous calculations neglected these mechanisms. We re-evaluate the bounds on
toroidally-compactified "gravity-only" dimensions (GODs), and find that
consistency with the observed SN1987a neutrino signal requires that if there
are two such dimensions then their radius must be less than 1 micron.
