1. A method of adaptive echo cancellation in a voice messaging or voice response system having a memory store, at least one digital signal processor, a digital voice data receive data line, a transmit data line, and an echo canceller apparatus comprising a digital adapt filter having a plurality of adapt filter coefficients, a digital cancel filter coupled to the adapt filter and an adaptation control means for controlling transfer of the adapt filter coefficients to the cancel filter, the method comprising the steps of: identifying a successive quantity of voice data frames on the transmit data line which pass a power criterion and storing the frames in a buffer; truncating a plurality of segments from each data frame, and for each segment, deriving adapt filter coefficients from a plurality of taps in each segment during all available computing cycles of the digital signal processor; selecting successive adjacent windows of taps from the adapt filter coefficents and identifying by an energy level test the best window; and transferring adapt filter coefficients in the best window to the cancel filter.