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This paper presents new efficient algorithms for implementing 3-D Crank-Nicolson-based finite-difference time-domain (FDTD) methods. Two recent methods are considered, namely, the Crank-Nicolson direct-splitting (CNDS) and Crank-Nicolson cycle-sweep-uniform (CNCSU) FDTD methods. The algorithms involve update equations whose right-hand sides are much simpler and more concise than the original ones. Analytical proof is provided to show the equivalence of original and present methods. Comparison of their implementations signifies substantial reductions of the floating-point operations count in the new algorithms. Other computational aspects are also optimized, particularly in regard to the for-looping overhead and the memory space requirement. Through numerical simulation and Fourier stability analysis, it is found that while the CNDS FDTD is unconditionally stable, the CNCSU FDTD may actually become unstable.