Compression of ultrasonic pulses reflected from layered structures is studied. A short pulse is emitted into water towards a structure consisting of solid plates backed with an air layer. Due to multiple reflections in the structure, the signal is elongated. The reflected signal is received by the same transducer and digitized. After that, the wave is reversed in time and emitted towards the layered structure for the second time; then, the reflected signal is received. Due to the invariance of the processes under the time reversal, the pulse is compressed by the structure: the reflected signal becomes shorter and acquires the waveform of the initial pulse. The possibility of an efficient compression of signals is demonstrated experimentally. Numerical simulations show that the use of more complex structures can considerably increase the compression ratio and produce short signals of a much higher amplitude than that emitted by the transducer. An efficient compression algorithm is proposed.