We present a model of bi-phasic vesicle in the limit of large surface tension. In this regime, the vesicle is completely stretched and well described by two spherical caps with a fold which concentrates the membrane stress. The conservation laws and geometric constraints restrict the space of possible shapes to a pair of solutions labeled by a parameter $\tau$ given by {\it line tension/pressure}. For a given $\tau$ value, the two solutions differ by the length of the interface between domains. For a critical value $\tau_c$ , the two vesicle shapes become identical and no solution exists above this critical value. This model sheds new light on two proposed mechanisms (osmotic shocks and molecule absorption) to explain the budding and the fission in recent experiments.