Recently a lattice structure for adaptive linear prediction using the least mean square gradient approach was proposed. This paper investigates the application of this method to speech signals, and presents a number of implementations of the Adaptive Lattice Linear Prediction (ALLP) algorithm. These implementations allow flexible tradeoffs to be made between the computational requirements and the covergence properties of the algorithm. A measure of fast spectral transitions, inherent in certain implementations, is also described with particular application to detecting plosives in speech. Experimental results are discussed.