Non-planar GaInN/GaN light-emitting diodes were epitaxially grown to exhibit steps for enhanced light emission. By means of a large off-cut of the epitaxial growth plane from the c-plane (0.06° to 2.24°), surface morphologies of steps and inclined terraces that resemble fish scale patterns could controllably be achieved. These patterns penetrate the active region without deteriorating the electrical device performance. We find conditions leading to a large increase in light-output power over the virtually on-axis device and over planar sapphire references. The process is found suitable to enhance light extraction even without post-growth processing.