  In this paper we prove a formula, much in the spirit of one due to Rubin,
which expresses the leading coefficients of various p-adic L-functions in the
presence of an exceptional zero in terms of Nekovar's p-adic height pairings on
his extended Selmer groups. In a particular case, the Rubin-style formula we
prove recovers a p-adic Kronecker limit formula. In a disjoint case, we observe
that our computations with Nekovar's heights agree with the Ferrero- Greenberg
formula (more generally, Gross' conjectural formula) for the leading
coefficient of the Kubota-Leopoldt p-adic L-function (resp., the Deligne-Ribet
p-adic L-function) at s = 0.
