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Semantic parsing is a key NLP task that maps natural language to structured meaning representations. As in many other NLP tasks, SOTA performance in semantic parsing is now attained by fine-tuning a large pretrained language model (PLM). While effective, this approach is inefficient in the presence of multiple downstream tasks, as a new set of values for all parameters of the PLM needs to be stored for each task separately. Recent work has explored methods for adapting PLMs to downstream tasks while keeping most (or all) of their parameters frozen. We examine two such promising techniques, prefix tuning and bias-term tuning, specifically on semantic parsing. We compare them against each other on two different semantic parsing datasets, and we also compare them against full and partial fine-tuning, both in few-shot and conventional data settings. While prefix tuning is shown to do poorly for semantic parsing tasks off the shelf, we modify it by adding special token embeddings, which results in very strong performance without compromising parameter savings.