We present an investigation on the effect of inter-micellar connections (branches) on the rheology of wormlike micelles. The system chosen is made of lecithin, minute amounts of water and organic solvents. Lecithin and water self-assemble into wormlike reverse micelles that can be branched or unbranched depending on the oil composition (and on the water content). In this respect, cyclohexane favours disconnected reverse micelles while isooctane promotes the formation of branches. By using mixtures of cyclohexane and isooctane as the oil phase and different water/lecithin ratios, the branch density of the system can be finely tuned. PGSE-NMR experiments allowed us to distinguish between branch-free (unbranched) and branched systems and the response of the very same samples to mechanical stress was measured by rheology. This allows, for the first time, an experimental correlation between rheological properties and the presence of branches. It turned out that the presence of a few inter-micellar connections sensibly decreases the zero-shear viscosity measured in steady state flow curves. Comparison with oscillatory rheology experiments indicates that the main effect of branches is to shorten the terminal relaxation time by speeding-up the reptation