Current methods of cross-lingual parser transfer focus on predicting the best\nparser for a low-resource target language globally, that is, "at treebank\nlevel". In this work, we propose and argue for a novel cross-lingual transfer\nparadigm: instance-level parser selection (ILPS), and present a\nproof-of-concept study focused on instance-level selection in the framework of\ndelexicalized parser transfer. We start from an empirical observation that\ndifferent source parsers are the best choice for different Universal POS\nsequences in the target language. We then propose to predict the best parser at\nthe instance level. To this end, we train a supervised regression model, based\non the Transformer architecture, to predict parser accuracies for individual\nPOS-sequences. We compare ILPS against two strong single-best parser selection\nbaselines (SBPS): (1) a model that compares POS n-gram distributions between\nthe source and target languages (KL) and (2) a model that selects the source\nbased on the similarity between manually created language vectors encoding\nsyntactic properties of languages (L2V). The results from our extensive\nevaluation, coupling 42 source parsers and 20 diverse low-resource test\nlanguages, show that ILPS outperforms KL and L2V on 13/20 and 14/20 test\nlanguages, respectively. Further, we show that by predicting the best parser\n"at the treebank level" (SBPS), using the aggregation of predictions from our\ninstance-level model, we outperform the same baselines on 17/20 and 16/20 test\nlanguages.\n