We consider speech dialogues, allowing for simultaneous input (via speech recognition) and output (via speech synthesis or pre-recorded prompts), often referred to as "barge in". We start with a collection of dialogue situations, where simultaneous input and output is useful. It is argued, that a variety of possible system behaviour is necessary in order to take into account these situations adequately. We then define a formalism, that allows to control this system behaviour. We end up with reporting some experience gathered both in lab tests and a in real world pilot.