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A common problem in waveform design is to adapt the transmitted signal to the target environment in order that the interference from extended fields of scatterers is reduced. This problem is investigated here for the special case of detection of a single target in the ``vicinity'' of an extended clutter space. The paper considers the possibility of confining the matched-filter response in delay and Doppler, or ambiguity function, to a narrow strip with arbitrary orientation in the delay-Doppler plane. It is shown that strict confinement of the response is achievable only with waveforms that are unlimited in both time and frequency domain. With practical waveforms, which are necessarily of finite extent, one merely can trade close-target separability against detectability in the background clutter. Thus, one form of the resolution problem is exchanged against the other. The paper examines these effects quantitatively.