Abstract Thresholding a measure in conditional independence (CI) tests using a fixed value enables learning and removing edges as part of learning a Bayesian network structure. However, the learned structure is sensitive to the threshold that is commonly selected: 1) arbitrarily; 2) irrespective of characteristics of the domain; and 3) fixed for all CI tests. We analyze the impact on mutual information – a CI measure – of factors, such as sample size, degree of variable dependence, and variables’ cardinalities. Following, we suggest to adaptively threshold individual tests based on the factors. We show that adaptive thresholds better distinguish between pairs of dependent variables and pairs of independent variables and enable learning structures more accurately and quickly than when using fixed thresholds.