Stock price rallies/declines often terminate at price levels that are interpreted by many as areas of psychological resistance or support, while an alternative interpretation is that they coincide with price clusters. Some of these price levels tend to repeat with a regularity that is inconsistent with mere chance. In this paper, the existence of price clusters and psychological barriers is tested on a sample of 20 Australian stocks. We consider two number sequences, both derived from a base number of 100, as well as integer price levels. It is shown that Australian stock price data are not uniformly distributed and that for the majority of the stocks, price swing highs and lows are associated with certain recurring price levels. Some of the implications for trading and investing are considered.