Increasingly many applications utilize network-based solutions these days, such as cloud computing or Internet of Things technologies. Processing private data in various applications over the Internet raises concerns about the user privacy. These concerns may be solved by using novel cryptographic  methods, of which garbling schemes is one. Side-information is a key concept for defining the security of garbling schemes since it tells what is allowed to be leaked about the garbled evaluation. Current definitions have a full support to logic circuits while the concept of a garbling scheme should encompass all garbling techniques independent of the model of computation. In this paper, we improve the definition of side-information to fit any computation model, especially Turing machines. Moreover, we show that our definition of side-information also describes better the various threats against the security of garbling schemes, including possible side-channel attacks. We also demonstrate that the new definition has also the following advantages compared to the existing definitions. Our model of side-information supports a wider set of applications, including partial garbling schemes. Our model simplifies the security definitions of garbling schemes without compromising the existing results about the security relations of garbling schemes.