We propose a deep Convolutional Neural Network (CNN) for land cover mapping in remote sensing images, with a focus on urban areas. In remote sensing, class imbalance represents often a problem for tasks like land cover mapping, as small objects get less prioritised in an effort to achieve the best overall accuracy. We propose a novel approach to achieve high overall accuracy, while still achieving good accuracy for small objects. Quantifying the uncertainty on a pixel scale is another challenge in remote sensing, especially when using CNNs. In this paper we use recent advances in measuring uncertainty for CNNs and evaluate their quality both qualitatively and quantitatively in a remote sensing context. We demonstrate our ideas on different deep architectures including patch-based and so-called pixel-to-pixel approaches, as well as their combination, by classifying each pixel in a set of aerial images covering Vaihingen, Germany. The results show that we obtain an overall classification accuracy of 87%. The corresponding F1- score for the small object class "car" is 80.6%, which is higher than state-of-the art for this dataset.