We introduce the notion of LImited Memory Influence Diagram (LIMID) to describe multistage decision problems in which the traditional assumption of no forgetting is relaxed. This can be relevant in situations with multiple decision makers or when decisions must be prescribed under memory constraints, such as in partially observed Markov decision processes (POMDPs). We give an algorithm for improving any given strategy by local computation of single policy updates and investigate conditions for the resulting strategy to be optimal.