Properties of electrostatically self-focused electron streams are calculated from stream injection parameters. The unneutralized ion density within the stream can be nearly an order of magnitude greater than that of stream particles alone. This effect is due to ionization by stream particles and collective behaviour of the stream and ambient plasma. Cold, uniform streams can occur only where stream linear density is sufficiently high. In certain cases ion cluster and molecular ion formation give rise to tight focusing. Periodic self-focusing provides axial electric fields which can resonantly drive stream particle oscillations and which can be used for acceleration of ambient ions.