This study explores the feasibility of sensitive machines; that is, machines with empathic abilities, at least to some extent. A signal processing and machine learning pipeline is presented that is used to analyze data from two studies in which 25 Post-Traumatic Stress Disorder (PTSD) patients participated. The feasibility of speech as a stress detector was validated in a clinical setting, using the Subjective Unit of Distress (SUD). 13 statistical parameters were derived from five speech features, namely: amplitude, zero crossings, power, high-frequency power, and pitch. To achieve a low dimensional representation, a subset of 28 parameters was selected and, subsequently, compressed into 11 principal components (PC). Using a Multi-Layer Perceptron neural network (MLP), the set of 11 PC were mapped upon 9 distinct quantizations of the SUD. The MLP was able to discriminate between 2 stress levels with 82.4% accuracy and up to 10 stress levels with 36.3% accuracy. With stress baptized as being the black death of the 21st century, this work can be conceived as an important step towards computer aided mental health care.