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Quantum computing is on the cusp of reality with Noisy Intermediate-Scale Quantum (NISQ) machines currently under development and testing. Some of the most promising algorithms for these machines are variational algorithms that employ classical optimization coupled with quantum hardware to evaluate the quality of each candidate solution. Recent work used GRadient Descent Pulse Engineering (GRAPE) to translate quantum programs into highly optimized machine control pulses, resulting in a significant reduction in the execution time of programs. This is critical, as quantum machines can barely support the execution of short programs before failing. However, GRAPE suffers from high compilation latency, which is untenable in variational algorithms since compilation is interleaved with computation. We propose two strategies for partial compilation, exploiting the structure of variational circuits to pre-compile optimal pulses for specific blocks of gates. Our results indicate significant pulse speedups ranging from 1.5x-3x in typical benchmarks, with only a small fraction of the compilation latency of GRAPE.