The competition between adhesion and tether formation in bound vesicles is investigated. A theoretical model is developed in which tethers are induced by the application of a pulling force to the top of a strongly adhered vesicle. A critical onset force is identified where the tether spontaneously appears as part of a first order shape transition. Further growth of the tether initiates a detachment process that culminates in a continuous unbinding of the vesicle at a finite detachment force. Both critical forces, as well as all shape parameters, are calculated as a function of the reduced volume and the strength of adhesive potential.