The Order-Preserving SubMatrices (OPSMs) are employed to discover significant biological associations between genes and experiment conditions. Herein, we propose a new relaxed OPSM model by considering the linearity relaxation, which is called the Bucket OPSM (BOPSM) model. An efficient method called ApriBopsm is developed to exhaustively mine such BOPSM patterns. We further generalize the BOPSM model by incorporating the similarity relaxation strategy. We develop a generalized BOPSM model called GeBOPSM and adopt a pattern growing method called SeedGrowth to mine GeBOPSM patterns. Informally, the SeedGrowth algorithm adopts two different growing strategies on rows and columns in order to expand a seed BOPSM into a maximal GeBOPSM pattern. We conduct a series of experiments using both synthetic and biological datasets to study the effectiveness of our proposed relaxed models and the efficiency of the relevant mining methods. The BOPSM model is shown to be able to capture the characteristics of noisy OPSM patterns, and is superior to the strict counterparts. ApriBopsm is also significantly more efficient than OPC-Tree, which is the state-of-the-art OPSM mining method. Compared to all the current relaxed OPSM models, the GeBOPSM model achieves the best performance in terms of the number of mined quality patterns.