A lookup engine of a transactional memory (TM) has multiple hardware lookup structures, each usable to perform a different type of lookup. In response to a lookup command, the lookup engine reads a first block of first information from a memory unit. The first information configures the lookup engine to perform a first type of lookup, thereby identifying a first result value. If the first result value is not a final result value, then the lookup engine uses address information in the first result value to read a second block of second information. The second information configures the lookup engine to perform a second type of lookup, thereby identifying a second result value. This process repeats until a final result value is obtained. The type of lookup performed is determined by the result value of the preceding lookup and/or type information of the block of information for the next lookup.