LLMs are highly sensitive to prompt design, but handcrafting effective prompts is difficult and often requires intricate crafting of few-shot examples. We propose a fast automatic prompt construction algorithm that augments human instructions by generating a small set of few shot examples. Our method iteratively replaces/drops/keeps few-shot examples using Monte Carlo Shapley estimation of example utility. For faster execution, we use aggressive subsampling and a replay buffer for faster evaluations. Our method can be run using different compute time budgets. On a limited budget, we outperform existing automatic prompting methods on text simplification and GSM8K and obtain second best results on classification and summarization. With an extended, but still modest compute budget we set a new state of the art among automatic prompting methods on classification, simplification and GSM8K. Our results show that carefully constructed examples, rather than exhaustive instruction search, are the dominant lever for fast and data efficient prompt engineering. Our code is available at https://github.com/Batorskq/PIAST.