Abstract A general result is derived, allowing the transformation of incoherent constant false alarm rate detection processes from a given clutter environment to that of any clutter model of interest. This generalises recent work where detection processes for Pareto distributed clutter are developed in a similar way. The approach preserves the original probability of false alarm and threshold multiplier relationship. To illustrate the application of the method, a simple example is considered for target detection in uniformly distributed clutter. An extensive application to target detection in Weibull distributed clutter is presented, with the focus being on producing transformed detectors to run on real X-band maritime surveillance radars.