A simple perturbation method is used to study fluxon (soliton) interactions on a Josephson transmission line (JTL). This technique efficiently provides information needed in the design of JTL computer circuits. We study (i) fluxons interacting with other fluxons in the presence of both dissipation and an externally controlled current bias and (ii) fluxons interacting with microshorts. The dynamics of fluxon pinning to a microshort is described and threshold conditions for fluxon-antifluxon annihilation are presented. We emphasize that in this process free fluxons become bound into "breathers", which in turn decay into "photons" of the Josephson waveguide.