3D texture-based volume rendering is a popular way of realizing direct volume visualization on graphics hardware. However, the slice-oriented texture memory layout of many current GPUs may lead to a strongly view-dependent performance, which reduces the fields of application of volume rendering. In this short technical note, we propose a slight modification of texture-based volume rendering that maintains roughly constant frame rates on any GPU architecture. The idea is to split the volume into smaller subvolumes. These bricks can be oriented in different directions; thus the varying performance for different viewing directions is averaged out.