  It is shown that for any elastic string model with energy density $U$ and
tension $T$, the divergent contribution from gravitational self interaction can
be allowed for by an action renormalisation proportional to $(U-T)^2$. This
formula is applied to the important special case of a bare model of the
transonic type (characterised by a constant value of the product $UT$) that
represents the macroscopically averaged effect of shortwavelength wiggles on an
underlying microscopic model of the Nambu-Goto type (characterised by $U=T$).
