A method for detection of Gaussian signals with uncertain bandwidth in a background of stationary, white Gaussian noise is proposed. The proposed method is designed to improve over conventional energy detection, for which a signal bandwidth must be assumed. The method proposed here does not rely on estimates of signal parameters other than specifying a range of anticipated bandwidth, making it suitable for short duration signals. The performance of the proposed method is measured by the probability of detection for a given false-alarm probability and is compared with conventional energy detection.<<ETX>>