The three-dimensional structure and decay of a dipolar vortex in a linearly stratified fluid is investigated experimentally using a high-resolution three-dimensional scanning correlation image velocimetry system (SCIV). Comparisons with simple theoretical and numerical models are made for late times in the low-Froude-number regime. The relatively well-known stratified dipole, most of the time assumed to be quasi-two-dimensional, is revealed to have a complex three-dimensional vortex topology arising from its self-induced propagation. As the buoyancy scale $u/N$ approaches zero the dynamics of such a structure are dominated by the horizontal velocity field, whereas the diffusion is mainly vertical. The evolution is then governed by an effective Reynolds number, $\hbox{\it Re}_{\hbox{\scriptsize{\it eff}}}$, based on vertical diffusion and horizontal advection. At early times this effective Reynolds number is large, horizontal advection terms dominate and a decrease of aspect ratio of the structure is observed until $\hbox{\it Re}_{\hbox{\scriptsize{\it eff}}}$ reaches a critical value $\hbox{\it Re}_{\hbox{\scriptsize{\it eff}}}^c \,{\sim}\, O(1)$, independent of the initial condition and associated with a horizontal advection–vertical diffusion balance. Thereafter the evolution becomes purely diffusive with decay time $\hbox{\it Re}_{\hbox{\scriptsize{\it eff}}}^c$.