The inferred cost of work-related stress call for prevention strategies that aim at detecting early warning signs at the workplace. This paper goes one step towards the goal of developing a personal health system for detecting stress. We analyze the discriminative power of electrodermal activity (EDA) in distinguishing stress from cognitive load in an office environment. A collective of 33 subjects underwent a laboratory intervention that included mild cognitive load and two stress factors, which are relevant at the workplace: mental stress induced by solving arithmetic problems under time pressure and psychosocial stress induced by social-evaluative threat. During the experiments, a wearable device was used to monitor the EDA as a measure of the individual stress reaction. Analysis of the data showed that the distributions of the EDA peak height and the instantaneous peak rate carry information about the stress level of a person. Six classifiers were investigated regarding their ability to discriminate cognitive load from stress. A maximum accuracy of 82.8% was achieved for discriminating stress from cognitive load. This would allow keeping track of stressful phases during a working day by using a wearable EDA device.