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This paper develops a general framework for the construction of simple (or path-independent) multinomial lattice approximations to single-state variable diffusion processes. It reexamines, within this general framework, three simple lattice procedures for the pricing of interest rate-contingent claims. These procedures include the Nelson and Ramaswamy (NR 1990) binomial model, the Tian (1992) simplified binomial (SB) model, and the Hull and White (HW 1990b) trinomial model. Particular attention is paid to the application of these procedures to the pricing of interest rate-contingent claims when the short-term interest rate follows the stochastic process developed by Cox, Ingersoll, and Ross (CIR 1985b). It is argued that the HW and the SB models do not always converge, while the NR model always does. The condition under which the HW and the SB models do converge is also examined. Finally, the numerical accuracy and computational efficiency of the three procedures are investigated through a simulation experiment. These procedures are implemented to value zero-coupon bonds and call options on zero-coupon bonds when the interest rate follows the CIR process. The results have clear implications for users of numerical procedures: When convergence is assured, the HW or SB model is preferred since these models are computationally more efficient than the NR model; otherwise, the NR model should be used. For the CIR process, empirically estimated parameters rarely violate the convergence condition; thus the convergence property of the HW and SB model is moot.