We propose the braiding of optical vortices in a laser beam with more than 2 π rotation by superposing Bessel modes with a plane wave. We experimentally demonstrate this by using a Bessel–Gaussian beam and a coaxial Gaussian, and we present measurements of three complete braids. The amount of braiding is fundamentally limited only by the numerical aperture of the system, and we discuss how braiding can be controlled experimentally for any number of vortices.