This paper evaluates the degree to which active methods can be used to reduce the level of sound‐pressure fluctuations in an enclosure excited at low frequencies by a stationary random source. The spectral density of the total acoustic potential energy in the enclosure is used as a cost function for evaluating the global effectiveness of the technique. The enclosure is controlled by a secondary source whose output is constrained to act causally with respect to the primary source. The optimal causal filter relating the secondary source output to the primary source output can be deduced using classical Wiener filter theory. A numerical approach is adopted for the solution of the resulting Wiener–Hopf integral equation. It is shown that the resonances of the enclosure can be successfully suppressed by the action of the active control.