In this paper we study the broadcast problem in wireless networks when the broadcast is helped by a labelling scheme. Our contribution is twofold. First, we propose label optimal broadcast algorithms in a class of networks issued from our recent studies in wireless body area networks. We refer to these networks (level separable networks). We focus on two variants of broadcast: broadcast without acknowledgement (i.e. the initiator of the broadcast is not notified at the end of broadcast) and broadcast with acknowledgement. We propose an acknowledgement-free broadcast strategy using 1-bit labelling and broadcast with acknowledgement using a 2-bit labelling. In the class of level-separable networks our algorithms are memory optimal and finish within 2D rounds for both broadcast with and without acknowledgement, where D is the eccentricity of the broadcast initiator. In the broadcast with acknowledgement, we trigger the acknowledgement message during the broadcast propagation such that no extra rounds are needed for sending the acknowledgement back to the source once the broadcast is finished. Second, we improve a recent labelling-based broadcast scheme with acknowledgement designed for arbitrary networks in terms of memory and time complexity. That is, we better exploit the encoding of labels in order to not use extra memory to carry back the acknowledgement to the source. Nodes store only a 3-bits labelling.