Abstract-During initialization, discrete multitone receivers train a time domain equalizer (TEQ) to shorten the channel impulse response to a preset length, ν + 1. Arslan, Kiaei, and Evans report a Minimum Intersymbol Interference (Min-ISI) method for TEQ design. Min-ISI TEQs give the highest bit rates among single-FIR TEQs amenable to real-time implementation on programmable fixed-point digital signal processors (DSPs). The Min-ISI method, however, has several disadvantages: (1) sensitivity to transmission delay, (2) inability to design TEQs longer than ν + 1 taps, and (3) sensitivity to the fixed-point computation in the Cholesky decomposition. In this paper, we develop an alternate Min-ISI cost function, from which we derive (1) a fast search method for the optimal transmission delay, (2) extensions to design arbitrary-length Min-ISI TEQs, and (3) an iterative Min-ISI method. The iterative Min-ISI method avoids Cholesky decomposition, designs arbitrary length TEQs, and achieves the bit rate performance of the original Min-ISI method.