Utterances such as "Megan ate some of the cupcakes" are often interpreted as "Megan ate some but not all of the cupcakes". Such an interpretation is thought to arise from a pragmatic inference called scalar implicature (SI). Preschoolers typically fail to spontaneously generate SIs without the assistance of training or context that make the stronger alternative salient. However, the exact role of alternatives in generating SIs remains contested. Specifically, it is not clear whether children have difficulty with spontaneously generating possible informationally stronger scalemates, or with considering how alternatives might be relevant. We present three studies with English-speaking 5-year-olds and adults designed to address these questions. We show that (a) the accessibility of the stronger alternative is important for children's SI generation (Experiment 1); (b) the explicit presence of the stronger alternative leads children to generate SIs only when the stronger scalar term can easily be seen as relevant (Experiment 2); and (c) in contexts that establish relevant alternatives, the explicit presence of the stronger alternative is not necessary (Experiment 3). We conclude that children's considerations of lexical alternatives during SI-computation include an important role for conversational relevance. We also show that this more nuanced approach to the role of lexical alternatives in pragmatic inference unifies previously unconnected findings about children's early pragmatic development and bears on major accounts proposed to date for children's problems with SIs.