The development of informative, admissible heuristics for cost-optimal planning remains a significant challenge in domain-independent planning research. Two techniques are commonly used to try to improve heuristic estimates. The first is disjunction: taking the maximum across several heuristic values. The second is the use of additive techniques, taking the sum of the heuristic values from a set of evaluators in such a way that admissibility is preserved. In this paper, we explore how the two can be combined in a novel manner, using disjunction within additive heuristics. We define a general structure, the Additive-Disjunctive Heuristic Graph (ADHG), that can be used to define an interesting class of heuristics based around these principles. As an example of how an ADHG can be employed, and as an empirical demonstration, we then present a heuristic based on the well-known additive hm heuristic, showing an improvement in performance when additive-disjunctive techniques are used.