Many modern waste treatment processes and waste management systems are able to treat many different types of waste at the same time, and deliver a number of useful outputs (secondary materials, energy) as well. These systems are thus increasingly multi-functional. As such, in life cycle assessment studies, they create problems related to multi-functionality and allocation. Especially in LCAs of waste management systems, the solution in the form of system expansion or avoided burdens approach dominates the practice, and the partitioning approach plays a minor role. In this paper, we analyse the logic and problems of these two approaches. It appears that for the avoided burdens approach, the number of 'what-if' assumptions is so large that LCAs on the same topic lead to quite diverging results. Since 'what-if' questions cannot be answered in an unambiguous way, such questions should preferably be left outside of a primarily scientific tool. The partitioning approach is not free from arbitrary choices as well, but, in contrast to the 'what-if' approaches, it does not claim to predict what happens or what would have happened.