In three forced-choice completion experiments in Hebrew, the present study investigates the degree to which attachment decisions in sentences with local ambiguity are driven by the goal to maximize interpretation during incremental processing. In particular, we examine a processing strategy aimed at thematic assignment maximization proposed by Pritchett (1988, 1992): at every point during processing, the Theta Criterion attempts to be satisfied, given the maximal thematic grid of the available verbs. We find a consistent preference for attaching a noun phrase to a preceding verb over attaching it as the subject of a yet-unmentioned verb, in accord with thematic assignment maximization and in line with previous observations. In contrast, when two possible verbs were available before the noun phrase, no consistent attachment preference was observed. This points to a prominent role for thematic assignment in ambiguity resolution. In addition, transitivity bias was found to affect processing choices in the latter case, but not in the former. Finally, we show that local thematic assignment maximization can even override global grammaticality.