This paper is motivated by the vision of more efficient packet classification mechanisms that self-optimize in a demand-aware manner. At the heart of our approach lies a self-adjusting linear list data structure, where unlike in the classic data structure, there are dependencies, and some items must be in front of the others; for example, to correctly classify packets by rules arranged in a linked list, each rule must be in front of lower priority rules that overlap with it. After each access we can rearrange the list, similarly to Move-To-Front, but dependencies need to be respected. We present a 4-competitive online rearrangement algorithm, whose cost is at most four times worse than the optimal offline algorithm; no deterministic algorithm can be better than 3-competitive. The algorithm is simple and attractive, especially for memory-limited systems, as it does not require any additional memory (e.g., neither timestamps nor frequency statistics). Our approach can simply be deployed as a drop-in replacement for a static datastructure, potentially benefitting many existing networks. We evaluate our self-adjusting list packet classifier on realistic ruleset and traffic instances. We find that our classifier performs similarly to a static list for low-locality traffic, but significantly outperforms Efficuts (by a factor 7x), CutSplit (3.6x), and the static list (14x) for high locality and small rulesets. Memory consumption is 10x lower on average compared to Efficuts and CutSplit.