In a pipelined data processor, when a dependency is detected between a first instruction and a second, subsequent instruction, the second instruction is abandoned. A look-ahead mode of operation is then initiated, in which instructions subsequent to the abandoned instruction are allowed to continue to be executed so as to pre-fetch operands, but are not allowed to be fully executed. The processor has two separate streams of instructions, each of which streams can be independently put into look-ahead mode. When one stream is in look-ahead mode, the other is given priority.