Computationally efficient recursive-least-squares (RLS) procedures are presented specifically for the adaptive adjustment of the data-driven echo cancellers (DDEC's) that are used in voiceband fullduplex data transmission. The methods are shown to yield very short learning times for the DDEC, while they also simultaneously reduce computational requirements to below those required for other leastsquare procedures, such as those recently proposed by Salz (1983). The new methods can be used with any training sequence over any number of iterations, unlike any of the previous fast-Converging methods. The methods are based upon the fast transversal filter (FTF) RLS adaptive filtering algorithms that were independently introduced by the authors of this paper; however, several special features of the DDEC are introduced and exploited to further reduce computation to the levels that would be required for slower-converging stochastic-gradient solutions. Several tradeoffs between computation, memory, learning time, and performance are also illuminated for the new initialization methods.