Using a dual-task gait paradigm, a number of studies have reported a relationship between cognitive function and gait. However, it is not clear to what extent these effects are dependent on the type of cognitive and walking tasks used in the dual-task paradigm. This study examined whether stride time variability (STV) and trunk range of motion (RoM) are affected by the type of cognitive task and walking speed used during dual-task gait. Participants walked at both their preferred and 25% of their preferred walking speed and performed a serial subtraction and a working memory task at both speeds. Both dual-tasks significantly reduced STV at both walking speeds, but there was no difference between the two tasks. Trunk RoM was affected by the walking speed and type of cognitive task used during dual-task gait: medio-lateral trunk RoM was increased at the slow walking speed and anterior-posterior trunk RoM was higher when performing the serial subtraction task at the slow walking speed only. The reduction of STV, regardless of cognitive task type, suggests healthy adults may redirect cognitive processes away from gait toward cognitive task performance during dual-task gait.