Considering accessibility of the 3'UTR is believed to increase the precision of microRNA target predictions. We show that, contrary to common belief, ranking by the hybridization energy or by the sum of the opening and hybridization energies, used in currently available algorithms, is not an efficient way to rank predictions. Instead, we describe an algorithm which also considers only the accessible binding sites but which ranks predictions according to over-representation. When compared with experimentally validated and refuted targets in the fruit fly and human, our algorithm shows a remarkable improvement in precision while significantly reducing the computational cost in comparison with other free energy based methods. In the human genome, our algorithm has at least twice higher precision than other methods with their default parameters. In the fruit fly, we find five times more validated targets among the top 500 predictions than other methods with their default parameters. Furthermore, using a common statistical framework we demonstrate explicitly the advantages of using the canonical ensemble instead of using the minimum free energy structure alone. We also find that ‘naïve’ global folding sometimes outperforms the local folding approach.