A method which includes, in a processor that processes instructions of program code, processing one or more of the instructions in a first segment of the instructions by a first hardware thread. Upon detecting that an instruction defined as a parallelization point has been fetched for the first thread, a second hardware thread is invoked to process at least one of the instructions in a second segment of the instructions, at least partially in parallel with processing of the instructions of the first segment by the first hardware thread, in accordance with a specification of register access that is indicative of data dependencies between the first and second segments.