Like for many text understanding and generation tasks, pre-trained languages models have emerged as a powerful approach for extracting information from business documents. However, their performance has not been properly studied in data-constrained settings which are often encountered in industrial applications. In this paper, we show that LayoutLM, a pre-trained model recently proposed for encoding 2D documents, reveals a high sample-efficiency when fine-tuned on public and real-world Information Extraction (IE) datasets. Indeed, LayoutLM reaches more than 80% of its full performance with as few as 32 documents for fine-tuning. When compared with a strong baseline learning IE from scratch, the pre-trained model needs between 4 to 30 times fewer annotated documents in the toughest data conditions. Finally, LayoutLM performs better on the real-world dataset when having been beforehand fine-tuned on the full public dataset, thus indicating valuable knowledge transfer abilities. We therefore advocate the use of pre-trained language models for tackling practical extraction problems.