Assessing the significance of patterns in presence-absence data is an important question in ecological data analysis, e.g., when studying nestedness. Significance testing can be performed with the commonly used fixed-fixed models, which preserve the row and column sums while permuting the data. The manuscript considers the properties of fixed-fixed models and points out how their strict constraints can lead to limited randomizability. The manuscript considers the question of relaxing row and column sun constraints of the fixed-fixed models. The Rasch models are presented as an alternative with relaxed constraints and sound statistical properties. Models are compared on presence-absence data and surprisingly the fixed-fixed models are observed to produce unreasonably optimistic measures of statistical significance, giving interesting insight into practical effects of limited randomizability.