Surveys provide valuable insights into public opinion and behavior, but their execution is costly and slow.Large language models (LLMs) have been proposed as a scalable, lowcost substitute for human respondents, but their outputs are often biased and yield invalid estimates.We study the interplay between synthesis methods that use LLMs to generate survey responses and rectification methods that debias population estimates, and explore how human responses are best allocated between them.Using two panel surveys with questions on nutrition, politics, and economics, we find that synthesis alone introduces substantial bias (24-86%), whereas combining it with rectification reduces bias below 5% and increases effective sample size by up to 14%.Overall, we challenge the common practice of using all human responses for fine-tuning, showing that under a fixed budget, allocating most to rectification results in more effective estimation.