There is compelling evidence that context strongly influences our choice of words (e.g., whether we refer to a particular animal with the basic-level name “bird” or the subordinate-level name “duck”). However, little is known about whether the context already affects the degree to which the alternative words are activated. In this study, we explored the effect of a preceding linguistic context on the phonological activation of alternative picture names. In Experiments 1 to 3, the context was established by a request produced by an imaginary interlocutor. These requests either constrained the naming response to the subordinate level on pragmatic grounds (e.g., “name the bird!”) or not (e.g., “name the object!”). In Experiment 4, the context was established by the speaker’s own previous naming response. Participants named the pictures with their subordinate-level names and the phonological activation of the basic-level names was assessed with distractor words phonologically related versus unrelated to that name (e.g., “birch” vs. “lamp”). In all experiments, we consistently found that distractor words phonologically related to the basic-level name interfered with the naming response more strongly than unrelated distractor words. Moreover, this effect was of comparable size for nonconstraining and constraining contexts indicating that the alternative name was phonologically activated and competed for selection, even when it was not an appropriate lexical option. Our results suggest that the speech production system is limited in its ability of flexibly adjusting and fine-tuning the lexical activation patterns of words (among which to choose from) as a function of pragmatic constraints.