We analyze the use of images from face parts to estimate soft-biometrics indicators. Partial face occlusion is common in unconstrained scenarios, and it has become mainstream during the COVID-19 pandemic due to the use of masks. Here, we apply existing pre-trained CNN architectures, proposed in the context of the ImageNet Large Scale Visual Recognition Challenge, to the tasks of gender, age, and ethnicity estimation. Experiments are done with 12007 images from the Labeled Faces in the Wild (LFW) database. We show that such off-the-shelf features can effectively estimate soft-biometrics indicators using only the ocular region. For completeness, we also evaluate images showing only the mouth region. In overall terms, the network providing the best accuracy only suffers accuracy drops of 2-4% when using the ocular region, in comparison to using the entire face. Our approach is also shown to outperform in several tasks two commercial off-the-shelf systems (COTS) that employ the whole face, even if we only use the eye or mouth regions.