Since Pillsbury [1908. Attention. London: Swan Sonnenschein & Co], the issue of whether attention operates through inhibition or enhancement has been on the scientific agenda. We examined whether overcoming previous attentional inhibition or enhancement is the source of asymmetrical switch costs in spoken noun-phrase production and colour-word Stroop tasks. In Experiment 1, using bivalent stimuli, we found asymmetrical costs in response times for switching between long and short phrases and between Stroop colour naming and reading. However, in Experiment 2, using bivalent stimuli for the weaker tasks (long phrases, colour naming) and univalent stimuli for the stronger tasks (short phrases, word reading), we obtained an asymmetrical switch cost for phrase production, but a symmetrical cost for Stroop. The switch cost evidence was quantified using Bayesian statistical analyses. Our findings suggest that switching between phrase types involves inhibition, whereas switching between colour naming and reading involves enhancement. Thus, the attentional mechanism depends on the language-production task involved. The results challenge theories of task switching that assume only one attentional mechanism, inhibition or enhancement, rather than both mechanisms.