Summary: Limited lookahead supervision is a discrete-event systems framework in which control decisions are made by looking at finite-step projections of the behaviour of the system’s underlying automata. Projected system behaviour is represented as a lookahead tree with some depth limit decided on by the user. It can be difficult to strike a balance between the complexities associated with storing and analyzing the trees and the amount of information available to make decisions, both of which increase with depth. This paper considers the problem of accurately estimating the state space of lookahead trees with the intent of simplifying the process of determining a favourable depth to use. Although the estimation methods presented here apply cleanly to only certain kinds of automata, they also shed light onto the more complex behaviour of the others.