We study the connectivity of Bluetooth graphs, these are subgraphs of the random geometric graph model. There are two parameters that control the model: the radius r that determines the visible neighbors of each node, and the number of edges c that each node is allowed to have. The randomness comes from the distribution of nodes in space and the choices of each vertex. We characterize the connectivity threshold (in c) for values of r close the critical value for connectivity in the underlying random geometric graph. This is joint work with Nicolas Broutin, Luc Devroye and Gabor Lugosi.