In applications of direct -contact ultrasound, operating in pulse -echo mode, the transient resulting from the excitation of the transducer will mask any reflections from scatterers near the transducer surface. This results in a so called dead zone, preventing any defects to be detected. This is normally solved by introducing a delay line between the transducer and the specimen. There are drawbacks with this approach, and therefore we propose an alternative technique, which instead suppresses the transient from the excitation by a statistical modeling technique. This paper describes an algorithm for reduction of the dead zone and shows with experiments using both a single -element transducer and a 128 element linear array, that the transient from the transducer excitation can be suppressed sufficiently well to reveal side -drilled holes in a test block, which were previously masked.