Little empirical evidence is available regarding the effects of road traffic noise on cognitive performance in adults, although traffic noise can be heard at many offices and home office workplaces. Our study tested the impact of road traffic noise at different levels (50 dB(A), 60 dB(A), 70 dB(A)) on performance in three tasks that differed with respect to their dependency on attentional and storage functions, as follows: The Stroop task, in which performance relied predominantly on attentional functions (e.g., inhibition of automated responses; Experiment 1: n = 24); a non-automated multistage mental arithmetic task calling for both attentional and storage functions (Exp. 2: n = 18); and verbal serial recall, which placed a burden predominantly on storage functions (Experiment 3: n = 18). Better performance was observed during moderate road traffic noise at 50 dB(A) compared to loud traffic noise at 70 dB(A) in attention-based tasks (Experiments 1-2). This contrasted with the effects of irrelevant speech (60 dB(A)), which was included in the experiments as a well-explored and common noise source in office settings. A disturbance impact of background speech was only given in the two tasks that called for storage functions (Experiments 2-3). In addition to the performance data, subjective annoyance ratings were collected. Consistent with the level effect of road traffic noise found in the performance data, a moderate road traffic noise at 50 dB(A) was perceived as significantly less annoying than a loud road traffic noise at 70 dB(A), which was found, however, independently of the task at hand. Furthermore, the background sound condition with the highest detrimental performance effect in a task was also rated as most annoying in this task, i.e., traffic noise at 70 dB(A) in the Stroop task, and background speech in the mental arithmetic and serial recall tasks.