LLMs are increasingly used as seq2seq translators from natural language utterances to structured programs, a process called semantic interpretation. Unlike atomic labels or token sequences, programs are naturally represented as abstract syntax trees (ASTs). Such structured representation raises novel issues related to the design and selection of in-context examples (ICEs) presented to the LLM. We focus on decomposing the pool of available ICE trees into fragments, some of which may be better suited to solving the test instance. Next, we propose how to use (additional invocations of) an LLM with prompted syntax constraints to automatically map the fragments to corresponding utterances. Finally, we adapt and extend a recent method for diverse ICE selection to work with whole and fragmented ICE instances. We evaluate our system, SCUD4ICL, on popular diverse semantic parsing benchmarks, showing visible accuracy gains from our proposed decomposed diverse demonstration method. Benefits are particularly notable for smaller LLMs, ICE pools having larger labeled trees, and programs in lower resource languages.