Adaptive radar detection of point-like targets in presence of disturbance with unknown spectral properties is addressed. By relaxing the assumptions of the W-ABORT, a tunable detector with improved detection vs rejection trade-off is proposed. To this aim, the presence of a fictitious signal under the null hypothesis is modeled probabilistically, so that an additional degree of freedom is introduced in the statistic of the detector. The resulting parametric GLRT shows a range of possible behaviors, from Kelly's detector to the plain W-ABORT. Monte Carlo simulations reveal that an improved compromise can be obtained. Simple closed-form approximations are also given with near-optimal performance, so that the ultimate computational complexity remains comparable to that of the W-ABORT.