The paper was aimed at verifying the efficiency (from the informational point of view in the weak form) for the WIG20 index units and futures contracts listed on the Warsaw Stock Exchange. The first stage of the research consisted in the optimization of parameters for selected TA (Technical Analysis) instruments and techniques (moving averages, oscillators, trend movement indices, and volume-based techniques) that, on the basis of past data, permitted to obtain the best results for the instruments being tested.Next, the obtained daily average and weekly return rates were compared with the results of the 'buy& hold'-type check strategy. The obtained results show that on the basis of a number of past time series it is possible to construct an investment strategy that may permit to achieve over-average incomes. In this connection, thinking about the correctness of the hypothesis of efficiency of the market in the weak form put forward by Eugene Fama, one can come to the conviction that, even not being able to deny this hypothesis, one still can, in the light of the presented results, strongly shake this conception. Besides, a detailed analysis of the parameters optimizing the purchase/sale signals based on the most popular TA instruments leads to the conclusion that, in the practice of the Polish market of futures contracts listed on the Warsaw Stock Exchange, the techniques and parameters departing from the standard ones foreseen by the authors of the given TA instruments have proved more effective than the latter.