Frequency estimation for a single-tone complex exponential signal is a classical and fundamental problem in many applications, such as communications, radar, and power. Most DFT-based frequency estimators reported in the literature exhibit an error floor at high SNR, due to their use of approximations to nonlinear equations. This effect is pronounced for short observation windows. In this paper, we propose two simple nonlinear equation solvers for eliminating this error floor. Simulations confirm the effectiveness of this proposed approach. We add to the literature of DFT-based estimators by proposing a frequency estimator for the case where a measured sequence is zero-padded by a factor of two.