It is shown that a power law energy spectrum can be generated in a trap formed by shocks. Values for the rate of loss of particles from the trap are given and means of reducing these are discussed. Mirror velocities of the order of 10 000 to 1000 km/s are required to produce the observed spectrum, but these are needed in only a few of the traps in the accelerating region. It is shown that the increase in pressure of the relativistic gas in most circumstances sets a lower limit to the slope of the energy spectrum produced. This is used to explain the fact that the same spectrum is produced throughout the source. For one model the range of values of the radio spectrum are found to coincide with the maximum in the observed distribution of the radio spectra.