At Eurocrypt 2015, Zahur, Rosulek, and Evans proposed the model of Linear Garbling Schemes. This model proved a \(2\lambda \) -bit lower bound of ciphertexts for a broad class of garbling schemes. At Crypto 2021, Rosulek and Roy presented the innovative “three-halves” garbling scheme in which AND gates cost \(1.5\lambda +5\) bits and XOR gates are free. A noteworthy aspect of their scheme is the slicing-and-dicing technique, which is applicable universally to all AND gates when garbling a boolean circuit. Following this revelation, Rosulek and Roy presented several open problems. Our research primarily addresses one of them: “Is \(1.5\lambda \) bits optimal for garbled AND gates in a more inclusive model than Linear Garbling Schemes?” In this paper, we propose the Bitwise Garbling Schemes. Our key revelation is that \(1.5\lambda \) bits is indeed optimal for arbitrary garbled AND gates in our model. Moreover, we prove the necessity of the free-XOR technique: If free-XOR is forbidden, we prove a \(2\lambda \) -bit lower bound. As an extension, we apply our idea to construct a model for fan-in 3 gates. Somewhat unexpectedly, we prove a \(\frac{7}{4}\lambda \) -bit lower bound. Unfortunately, the corresponding construction is not suitable for 3-input AND gates.