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A robust methodology is presented for the accurate modal analysis of three-dimensional dielectric waveguides with the finite-difference time-domain (FDTD) method. We investigate the propagation of well-defined vector modes along strongly guiding rectangular waveguides. Eigensolutions of the vectorial wave equation are utilized in the simulations to accurately launch the fundamental and higher order eigenmodes. Results for their FDTD-computed propagation constant are found to be in excellent agreement with existing mode-solving techniques. Improved accuracy or significant computational savings are achieved when the nonstandard FDTD concepts are incorporated in the context of the present analysis.