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One major setback of thermoacoustic engines-when comparing them with ''conventional'' heat-engines or refrigerators-is their low power density. In this work a new attempt for achieving higher power densities was undertaken. The stack of a thermoacoustic engine, which usually consists of parallel plates much longer than the acoustic displacement amplitude, was substituted by parallel-plate segments, which were only a fraction of the displacement amplitude long and randomly orientated to each other. This alternative stack arrangement was expected to benefit from improved heat transfer characteristics and an anisotropic thermal conductivity. A simplified numerical model confirmed these expectations. Experiments with a thermoacoustic heat pump were carried out. The experimental results qualitatively agreed with the numerical model. At most, the power density was raised by approximately 50%. The coefficient of performance-defined as useful heat output divided by work input-increased by approximately one-third.