Linguistic acceptability judgments are widely agreed to reflect constraints on real-time language processing. Nonetheless, very little is known about how processing costs affect acceptability judgments. In this paper, we explore how processing limitations are manifested in acceptability judgment data. In a series of experiments, we consider how two factors relate to judgments for sentences with varying degrees of complexity: (1) the way constraints combine (i.e., additively or super-additively), and (2) the way a comprehender's memory resources influence acceptability judgments. Results indicate that multiple sources of processing difficulty can combine to produce super-additive effects, and that there is a positive linear relationship between reading span scores and judgments for sentences whose unacceptability is attributable to processing costs. These patterns do hold for sentences whose unacceptability is attributable to factors other than processing costs, e.g. grammatical constraints. We conclude that tests of (super)-additivity and of relationships to reading span scores can help to identify the effects of processing difficulty on acceptability judgments, although these tests cannot be used in contexts of extreme processing difficulty.