A common problem to signal processing are biases introduced by correlated noise. When quantifying time delays between two signals, mixed noise introduces a bias towards zero delay in conventional delay estimates based on the cross- or bispectrum. Here we propose two novel time delay estimators that address these shortcomings: (1) A cross-spectrum based approach that relies on estimating the periodicity of the phase spectrum rather than its slope, and (2) a bispectrum based approach, bispectral antisymmetrization, which removes contributions from not just Gaussian but all independent sources. In a simulation study, we compare conventional and novel TDE approaches and resolve differences in performance with respect to noise Gaussianity and auto-correlation structure. As a proof-of concept, we also perform TDE analysis on a neural stimulation dataset (n=3). We find that antisymmetrization consistently outperforms conventional bispectral methods at low signal-to-noise ratios (SNR) and prevents spurious zero-delay estimates in all mixed-noise environments. Time delay estimation based on phase periodicity also improves signal sensitivity compared to conventional cross-spectral methods. These observations are stable with respect to the magnitude of the delay and the statistical properties of the noise.