Automatic liver tumor segmentation would have a big impact on liver therapy planning procedures and follow-up assessment, thanks to standardization and incorporation of full volumetric information. In this work, we develop a fully automatic method for liver tumor segmentation in CT images based on a 2D fully convolutional neural network with an object-based postprocessing step. We describe our experiments on the LiTS challenge training data set and evaluate segmentation and detection performance. Our proposed design cascading two models working on voxel- and object-level allowed for a significant reduction of false positive findings by 85% when compared with the raw neural network output. In comparison with the human performance, our approach achieves a similar segmentation quality for detected tumors (mean Dice 0.69 vs. 0.72), but is inferior in the detection performance (recall 63% vs. 92%). Finally, we describe how we participated in the LiTS challenge and achieved state-of-the-art performance.