Aravind Joshi famously hypothesized that natural language syntax was characterized (in part) by mildly context-sensitive generative power. Subsequent work in mathematical linguistics over the past three decades has revealed surprising convergences among a wide variety of grammatical formalisms, all of which can be said to be mildly context-sensitive. But this convergence is not absolute. Not all mildly context-sensitive formalisms can generate exactly the same stringsets (i.e. they are not all weakly equivalent), and even when two formalisms can both generate a (...) certain stringset, there might be differences in the structural descriptions they use to do so. It has generally been difficult to find cases where such differences in structural descriptions can be pinpointed in a way that allows linguistic considerations to be brought to bear on choices between formalisms, but in this paper we present one such case. The empirical pattern of interest involves wh-movement dependencies in languages that do not enforce the wh-island constraint. This pattern draws attention to two related dimensions of variation among formalisms: whether structures grow monotonically from one end to another, and whether structure-building operations are conditioned by only a finite amount of derivational state. From this perspective, we show that one class of formalisms generates the crucial empirical pattern using structures that align with mainstream syntactic analysis, and another class can only generate that same string pattern in a linguistically unnatural way. This is particularly interesting given that (i) the structurally-inadequate formalisms are strictly more powerful than the structurally-adequate ones from the perspective of weak generative capacity, and (ii) the formalism based on derivational operations that appear on the surface to align most closely with the mechanisms adopted in contemporary work in syntactic theory (merge and move) are the formalisms that fail to align with the analyses proposed in that work when the phenomenon is considered in full generality. (shrink)