Significant difficulties in medical image segmentation include the high variability of images caused by their origin (multi-center), the acquisition protocols (multi-parametric), the variability of human anatomy, illness severity, the effect of age and gender, and notable other factors. This work addresses problems associated with the automatic semantic segmentation of lumbar spine magnetic resonance images using convolutional neural networks. We aimed to assign a class label to each pixel of an image, with classes defined by radiologists corresponding to structural elements such as vertebrae, intervertebral discs, nerves, blood vessels, and other tissues. The proposed network topologies represent variants of the U-Net architecture, and we used several complementary blocks to define the variants: three types of convolutional blocks, spatial attention models, deep supervision, and multilevel feature extractor. Here, we describe the topologies and analyze the results of the neural network designs that obtained the most accurate segmentation. Several proposed designs outperform the standard U-Net used as a baseline, primarily when used in ensembles, where the outputs of multiple neural networks are combined according to different strategies.