The problem of radar detection of a target echo embedded in Weibull clutter is addressed using MSMI and GLR techniques with the salient features of adaptive filtering and CFAR control. Although the GLR algorithm is robust for non-Gaussian interference, the MSMI algorithm is quite sensitive and gives rise to false alarms. To deal with non-Gaussian interference such as Weibull clutter, the `Gaussianing-whitening approach' is adopted since the MSMI and GLR algorithms were developed to operate in Gaussian interference environment.