Recently, privacy has become one of the hottest topics in the world of the Internet-based communications and computation. Many applications, such as cloud computing and various cloud services, require information security and privacy. However, in many cases the level of security in current solutions is insufficient. Methods to ensure secure multiparty computation have been studied for decades, but because of the needs of the modern computation this topic has recently become increasingly popular. Yao's garbled circuit is one method to compute a function f on an argument x privately without revealing any information about f and x except f(x). Unfortunately, current constructions for garbled circuits have limitations - either efficient construction at the cost of reusability or reusability at the cost of efficiency. In this paper we aim at somewhere between these two extremes by defining new security measures for garbling schemes. These definitions support design of reusable garbled circuits that achieve adaptive security even when the function argument is handled bitwise. Moreover, we show how the new classes are related to the existing security classes of garbling schemes. As a result, we obtain an extended hierarchy for the classes of garbling schemes.