People like Richard Dawkins and Douglas Hofstadter have suggested that for the analysis of complex biological systems, successful reductionism must involve coordinated efforts across a hierarchy of organizational levels. For example, to make sense of the behavior of a computer you can start with a software program like Internet Explorer and try to explain its functions in terms of the algorithms of the many software modules that were combined and packaged as a single application program. To explain how the software modules work you could explain how the upper level software program is implemented in the machine code of an actual computer. To explain the working of that computer you would have to describe the semiconductor and other components of the physical machine and how they execute machine language instructions. Ultimately you can explain the electronic components of the computer in terms of their physics.
Greedy reductionism is a good starting point for trying to explaining macroscopic systems. In statistical mechanics you can account for the macroscopic properties of gases in terms of molecules and their interactions. But for complex systems there are several hierarchical levels of chunking, organization and description between the physics and a coherent explanation of the interesting macroscopic behavior. It would be greedy reductionism to try to explain the behavior of your web browser only in terms of the movement of electrons. We may try to simply say "its all done with electrons", but a complete explanation must be considerably more sophisticated.
The opposite extreme from greedy reductionism is throwing up your hands and denying that a reductionistic analysis of a complex system can work at all. In his book Darwin's Dangerous Idea Dennett argues for the reasonable middle ground between giving up on reductionism and greedy reductionism.
See also: holism