Large Language Models (LLMs) often produce explanations that do not faithfully reflect the factors driving their predictions. In healthcare settings, such unfaithfulness is especially problematic: explanations that omit salient clinical cues or mask spurious shortcuts can undermine clinician trust and lead to unsafe decision support. We study how inference and training-time choices shape explanation faithfulness, focusing on factors practitioners can control at deployment. We evaluate three LLMs (GPT-4.1-mini, LLaMA 70B, LLaMA 8B) on two datasets-BBQ (social bias) and MedQA (medical licensing questions), and manipulate the number and type of few-shot examples, prompting strategies, and training procedure. Our results show: (i) both the quantity and quality of few-shot examples significantly impact model faithfulness; (ii) faithfulness is sensitive to prompting design; (iii) the instruction-tuning phase improves measured faithfulness on MedQA. These findings offer insights into strategies for enhancing the interpretability and trustworthiness of LLMs in sensitive domains.