This paper analyzes the degree of return predictability (or weak-form informational efficiency) of Dow Jones Islamic and conventional size and sector-indices using the data from 1996 to 2013. Employing the automatic portmanteau and variance ratio tests for the martingale difference hypothesis of asset returns, we find that all Islamic and conventional sub-index returns have been predictable in a number of periods, consistent with the implications of the adaptive markets hypothesis. Overall, the Islamic sector-indices exhibit a higher degree of informational efficiency than the conventional ones, especially in the Consumer Goods, Consumer Services, Financials and Technology sectors. We also find that the Islamic sub-indices tend to be more efficient than the conventional ones during crisis periods.