Methods and apparatuses for reducing the response time along with increasing the probability of ranging of optical rangefinders that digitize the signal waveforms obtained from the pulse echoes returned from various types of objects to be ranged, the pulse echoes being too weak to allow successful ranging from a single waveform or the objects being possibly in motion during the capture of the pulse echoes. In a first embodiment of the invention, the response time at close range of a digital optical rangefinder is reduced by using a signal averaging process wherein the number of data to be averaged varies with the distance according to a predetermined function. In a second embodiment of the invention, the probability of ranging objects in motion along the line of sight of a digital optical rangefinder is increased and the object velocity measured by performing a range shift of each acquired signal waveform prior to averaging. In a third embodiment of the invention, the signal waveforms acquired in the line of sight of a digital optical rangefinder are scanned over a predetermined zone and range shifted and averaged to allow for early detection and ranging of objects that enter in the zone.