Lightweight components are used in the design of modern lightweight ciphers. In the current paper, firstly we investigate a new family of lightweight $4\times 4$ almost MDS diffusion layers, mathematically, and determine when they are involutive. The proposed diffusion layers are suitable for software applications and have less fixed points, compared with the existent ones. Then, we examine the cryptographic properties of nonlinear components constructed by a 2-round Feistel scheme, theoretically, and propose some concrete examples of them, including lightweight hardware-oriented $8\times 8$ S-boxes. We compare the presented S-boxes with the ones in Midori-128.