A crimping tool to crimp a contact onto the end of a wire, the contact configured to receive both a stripped part and an insulated part of the wire end. The crimping tool includes a first and second tier to crimp the contact onto the conductor core and onto the insulating jacket of the wire respectively. A mechanism actuates the first and second tiers in substantially a simultaneous manner. At least one rotating element is arranged between at least one crimping component and a cam of at least one of the tiers, the rotating element possibly taking up at least two positions with respect to the crimping component. A crimping method crimps a contact both onto an insulating jacket of a wire and onto its conductor core.