The behaviour of wavefronts propagating in a tunnel with multiple, compact air chambers is investigated with particular reference to the suppression of unacceptable pressure disturbances radiating from exit portals. Attention is focussed primarily on chambers that respond in an over-damped manner to pressure variations in the tunnel. In the early part of the paper, comparisons are made between the qualitative behaviour of wavefront propagation in tunnels with and without air chambers. Thereafter, attention turns to a quantitative assessment of the influence of key design parameters, especially the chamber volume and properties of connectors between chambers and the tunnel. It is shown that the optimum type of connector depends upon the length of the tunnel along which the chambers exist. For short tunnels, relatively low-resistance connectors with linear pressure:flow rate characteristics are preferred, whereas for long tunnels, relatively high-resistance connectors with quadratic pressure:flow rate characteristics are likely to be more suitable. Brief attention is paid to the practical feasibility of creating suitable connectors.