Sycophancy, the tendency of large language models to favour user-affirming responses over critical engagement, has been identified as an alignment failure, particularly in high-stakes advisory and social contexts. While prior work has documented conversational features correlated with sycophancy, we lack a systematic understanding of what provokes or prevents AI sycophancy. Here, we present a set of controlled experimental studies where we first isolate how input framing influences sycophancy, and second, leverage these findings to develop mitigation strategies. In a nested factorial design, we compare questions to various non-questions where we vary three orthogonal factors: epistemic certainty (statement, belief, conviction), perspective (I- vs user-perspective), and affirmation vs negation. We show that (1) sycophancy is substantially higher in response to non-questions compared to questions. Additionally, we find that (2) sycophancy increases monotonically with epistemic certainty conveyed by the user, and (3) is amplified by I-perspective framing. Building on this, we show that asking a model to convert non-questions into questions before answering significantly reduces sycophancy. Importantly, this effect is stronger than a simple baseline prompt asking models "not to be sycophantic". Our work offers a practical and effective input-level mitigation that both developers and users can easily adopt.