This study investigates ultimate attainment at the syntax-discourse interface in adult second-language (L2) acquisition. In total, 91 L1 (first-language) English, L1 Dutch and L1 Russian advanced-to-near-native speakers of German and 63 native controls are tested on an acceptability judgement task and an on-line self-paced reading task. These centre on discourse-related word order optionality in German. Results indicate that convergence at the syntax-discourse interface is in principle possible in adult L2 acquisition, both in off-line knowledge and on-line processing, even for L1 English speakers, whose L1 does not correspond to L2 German in discourse-to-syntax mappings. At the same time, non-convergence of the L1 Dutch groups and differences in the L2 groups' performance between tasks suggest that asymmetries in L1-L2 discourse configurations and computational difficulties in mapping discourse onto syntax constrain L2 performance.