Using custom laser cavities to produce as the output some desired structured light field has seen tremendous advances lately, but there is no universal approach to designing such cavities for arbitrarily defined field structures within the cavity, e.g., at both the output and gain ends. Here we outline a general design approach for structured light from lasers which allows us to specify the required cavity for any selected structured light fields at both ends. We verify the approach by numerical simulation as well as by an unwrapped cavity experiment. The power of this approach is that the cavity can be designed to maximise the overlap with the available pump for higher powers, minimise thermal effects for higher brightness, and at the same time output a desired structured light field that may differ substantially from the gain-end profile. These benefits make this work appeal to the large laser communities interested in cavities for high brightness and/or customized output beams.