Extraction and subextraction tend to receive separate attention in syntax, which leads to the assumption that they should be analyzed independently, even though they both illustrate an asymmetry between subjects and objects. By looking at various phenomena in English, German, Spanish and Norwegian I propose that this parallel behavior is not accidental, but that there is a previously unnoticed generalization: subextraction is allowed iff extraction is possible and the target of subextraction is not an indirect object. I propose that a revised version of Spec-to-Spec antilocality (Erlewine 2016) is necessary: movement of and out of an XP must cross a Projection Line (PL) (Brody 1998), i.e. the set of all projections of a head. This version of antilocality can derive Freezing effects, Huang’s (1982) CED, and their exceptions; and Comp-trace effects and their neutralization, extending them to subextraction. However, antilocality on its own cannot derive the extraction-subextraction asymmetry in indirect objects. I propose that the Principle of Minimal Compliance (PMC) (Richards 1998) can suspend antilocality if agree between a probe and a goal has happened. The version adopted here will allow extraction of the whole XP, but disallow extraction of its specifier due to the lack of an agree relation. Antilocality and the PMC combined also make the right predictions in other domains such as the lack of do-support in matrix subject questions and A-movement of the subject in declarative clauses, providing evidence that antilocality is a constraint that should apply to (at least) both A and A’-movement.