TRASE is a k-space encoding method that uses RF transmit phase gradient fields to achieve mm-level resolution. However, image quality is critically dependent upon the efficient generation of B1 fields with uniform magnitude and strong phase gradients. We present a new family of phase gradient coil designs based upon a solenoid twisted about a transverse axis. Four twisted solenoids wound on a single cylindrical former are sufficient to encode two spatial dimensions. The design has many attractive geometric, electrical and magnetic characteristics, including the ability to encode in the B0-direction, previously not possible for transverse-B0 magnet geometries.