  It has recently been shown how the effect of the divergent part of the
gravitational self interaction for a classical string model in 4 dimensions can
be allowed for by a renormalisation of its stress energy tensor and in the
elastic case a corresponding renormalisation of the off shell action. It is
shown here that that it is possible to construct a new category of elastic
string models for which this effect is describable as a renormalisation in the
stricter ``formal'' sense, meaning that it only requires a rescaling of one of
the fixed parameters characterising the model.
