Our goal is twofold: 1) we want to mine the only statistically valid 2-itemsets out of a boolean datatable, 2) on this basis, we want to build the only higher-order non-redundant itemsets compared to their sub-itemsets. For the first task we have designed a randomization test (Tournebool) respectful of the structure of the data variables and independant from the specific distributions of the data. In our test set (959 texts and 8477 terms), this leads to a reduction from 126, 000 2-itemsets to 13, 000 significant ones, at the 99% confidence interval. For the second task, we have devised a hierarchical stepwise procedure (MIDOVA) for evaluating the residual amount of variation devoted to higher-order itemsets, yielding new possible positive or negative high-order relations. On our example, this leads to counts of 7,712 for 2-itemsets to 3 for 6-itemsets, and no higher-order ones, in a computationally efficient way.