As a recently consolidated paradigm for optimistic concurrency in modern multicore architectures, Transactional Memory (TM) can help to the exploitation of parallelism in irregular applications when data dependence information is not available up to runtime. This paper presents and discusses how to leverage TM to exploit parallelism in an important class of irregular applications, the class that exhibits irregular reduction patterns. In order to test and compare our techniques with other solutions, they were implemented in a software TM system called ReduxSTM, that acts as a proof of concept. Basically, ReduxSTM combines two major ideas: a sequential-equivalent ordering of transaction commits that assures the correct result, and an extension of the underlying TM privatization mechanism to reduce unnecessary overhead due to reduction memory updates as well as unnecesary aborts and rollbacks. A comparative study of STM solutions, including ReduxSTM, and other more classical approaches to the parallelization of reduction operations is presented in terms of time, memory and overhead.