This paper deals with the reassessment of the sample size for adaptive two stage designs based on conditional power arguments utilizing the variability observed at the first stage. Fisher's product test for the p-values from the disjoint samples at the two stages is considered in detail for the comparison of the means of two normal populations. We show that stopping rules allowing for the early acceptance of the null hypothesis which are optimal with respect to the average sample size may lead to a severe decrease of the overall power if the sample size is a priori underestimated. This problem can be overcome by choosing designs with low probabilities of early acceptance or by mid-trial adaptations of the early acceptance boundary using the variability observed in the first stage. This modified procedure is negligibly anti-conservative and preserves the power.

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