Evidence from dual-task performance indicates that speakers prefer not to select simultaneous responses in picture naming and another unrelated task, suggesting a response selection bottleneck in naming. In particular, when participants respond to tones with a manual response and name pictures with superimposed semantically related or unrelated distractor words, semantic interference in naming tends to be constant across stimulus onset asynchronies (SOAs) between the tone stimulus and the picture-word stimulus. In the present study, we examine whether semantic interference in picture naming depends on SOA in case of a task choice (naming the picture vs reading the word of a picture-word stimulus) based on tones. This situation requires concurrent processing of the tone stimulus and the picture-word stimulus, but not a manual response to the tones. On each trial, participants either named a picture or read aloud a word depending on the pitch of a tone, which was presented simultaneously with picture-word onset or 350 ms or 1000 ms before picture-word onset. Semantic interference was present with tone pre-exposure, but absent when tone and picture-word stimulus were presented simultaneously. Against the background of the available studies, these results support an account according to which speakers tend to avoid concurrent response selection, but can engage in other types of concurrent processing, such as task choices.