This paper introduces a new class of matching methods called Monotonic Imbalance Bounding (MIB), which generalizes and extends the existing Equal Percent Bias Reducing (EPBR) class. MIB methods are designed to bound imbalance in a more flexible and robust way than EPBR, which only guarantees expected balance. The paper analyzes the properties of MIB methods, particularly Coarsened Exact Matching (CEM), and demonstrates how they can improve causal inference compared to EPBR-based methods. MIB methods are defined by bounding the imbalance between treated and control units in a multivariate sense, using a generic function of the data and a distance metric. This allows for more precise control over imbalance, especially in complex datasets. Unlike EPBR, which focuses on expected balance, MIB methods focus on in-sample balance, which is more relevant for causal inference. The paper shows that MIB methods can achieve better balance on multiple variables simultaneously, without compromising balance on other variables. CEM is introduced as a specific member of the MIB class. It involves coarsening each variable into a small number of categories, then performing exact matching within each category. This approach ensures that the matched units are as similar as possible in terms of their pretreatment variables, leading to better balance. The paper demonstrates that CEM is a valid MIB method, as it satisfies the conditions for bounding imbalance in a multivariate sense. The paper also discusses the advantages of MIB methods over EPBR methods, particularly in terms of reducing model dependence and estimation error. MIB methods allow for more flexibility in controlling imbalance, which is crucial for causal inference. The paper provides analytical results and numerical simulations showing that MIB methods can significantly improve causal inference compared to EPBR-based methods. In conclusion, the paper presents a new class of matching methods, MIB, which generalizes and extends the EPBR class. MIB methods are more flexible and robust, allowing for better control over imbalance in complex datasets. The paper demonstrates that MIB methods, particularly CEM, can significantly improve causal inference compared to EPBR-based methods.This paper introduces a new class of matching methods called Monotonic Imbalance Bounding (MIB), which generalizes and extends the existing Equal Percent Bias Reducing (EPBR) class. MIB methods are designed to bound imbalance in a more flexible and robust way than EPBR, which only guarantees expected balance. The paper analyzes the properties of MIB methods, particularly Coarsened Exact Matching (CEM), and demonstrates how they can improve causal inference compared to EPBR-based methods. MIB methods are defined by bounding the imbalance between treated and control units in a multivariate sense, using a generic function of the data and a distance metric. This allows for more precise control over imbalance, especially in complex datasets. Unlike EPBR, which focuses on expected balance, MIB methods focus on in-sample balance, which is more relevant for causal inference. The paper shows that MIB methods can achieve better balance on multiple variables simultaneously, without compromising balance on other variables. CEM is introduced as a specific member of the MIB class. It involves coarsening each variable into a small number of categories, then performing exact matching within each category. This approach ensures that the matched units are as similar as possible in terms of their pretreatment variables, leading to better balance. The paper demonstrates that CEM is a valid MIB method, as it satisfies the conditions for bounding imbalance in a multivariate sense. The paper also discusses the advantages of MIB methods over EPBR methods, particularly in terms of reducing model dependence and estimation error. MIB methods allow for more flexibility in controlling imbalance, which is crucial for causal inference. The paper provides analytical results and numerical simulations showing that MIB methods can significantly improve causal inference compared to EPBR-based methods. In conclusion, the paper presents a new class of matching methods, MIB, which generalizes and extends the EPBR class. MIB methods are more flexible and robust, allowing for better control over imbalance in complex datasets. The paper demonstrates that MIB methods, particularly CEM, can significantly improve causal inference compared to EPBR-based methods.