Steerable Needles are novel devices that are capable of more complex pathways than conventional needles and are used to navigate through solid organs. They promise a number of benefits, including the ability to navigate around sensitive structures and reach difficult-to-access locations. However, there are limitations to current approaches. These include being limited by large turn radii, complex path planning necessitating robotic control, and causing damage to surrounding tissue which increases the risk of complications. In this work, we address these limitations with the design, modeling, and optimization of our tape spring steerable needle. We develop a mechanics-based model that predicts forces and performance. We also demonstrate the smallest turn radius for any steerable needle, in models and in real tissue. We characterize surrounding tissue damage and show that our design minimizes tissue damage relative to other devices. We optimize the performance of our device through model-informed design changes. Finally, we demonstrate various use cases and show that the tape spring steerable needle is a promising steerable needle approach that does not require complex path planning.