A sandwich detector composed of scintillator and steel-covered lead layers was introduced in the fixed-target COMPASS experiment at CERN for vetoing events not completely covered by the two-stage magnetic spectrometer. Wavelength shifting fibres glued into grooves in the scintillator tiles serve for fast readout. Minimum ionising particles impinging on the 2 m ×2 m detector outside of a central hole, sparing the spectrometer's entry, are detected with a probability of 98%. The response to charged particles and photons is modelled in detail in Monte Carlo calculations. Figures of merit of the veto trigger in 190 GeV/ c π − + p (or nucleus) experiments are an enrichment of exclusive events in the recorded data by a factor of 3.5 and a false-veto probability of 1%.