Ultrasonic sensing systems and associated methods provide side-lobe reduction to improve the acoustic detection of small objects, the signature envelope peaks of which can otherwise be obscured by subsidiary envelope peaks in side lobes that result from residual correlation between a signal received by an ultrasonic transducer and a template signal corresponding to a burst signal emitted by the ultrasonic transducer. A shaping signal by which the amplitude of the burst signal can be varied with respect to time is taken into account in the template signal, and correlator circuitry correlates a signal derived from the ultrasonic transducer with the template signal to produce a correlated output exhibiting the desired side-lobe reduction. The distance from the transducer to the detected object can thereby be determined with enhanced accuracy and responsiveness.