In-context learning (ICL) allows LLMs to learn from examples without changing their weights: this is a particularly promising capability for long-context LLMs that can potentially learn from many examples. Recently, Lin et al. (2024) proposed URIAL, a method using only three in-context examples to align base LLMs, achieving non-trivial instruction following performance. In this work, we show that, while effective, ICL alignment with URIAL still underperforms compared to instruction fine-tuning on established benchmarks such as MT-Bench and AlpacaEval 2.0 (LC), especially with more capable base LLMs. We then uncover the most relevant elements for successful in-context alignment, finding the crucial role of the decoding parameters. Based on these insights, we show that the approach of URIAL can indeed be improved by adding more, potentially carefully selected, high-quality demonstrations in context, getting closer to the performance of instruct models. Finally, we provide the first, to our knowledge, systematic comparison of ICL and instruction fine-tuning (IFT) for instruction following in the low data regime. Overall, our work advances the understanding of ICL as an alignment technique and its relationship to IFT.