We recently found a significant bias between spectral diffuse attenuation coefficient (Kd(λ)) retrievals by common ocean color algorithms and measurements from profiling floats [Remote. Sens.14, 4500 (2022)10.3390/rs14184500]. Here we show, using a multi-satellite match-up dataset, that the bias is markedly reduced by simple "tuning" of the algorithm's empirical coefficients. However, while the float dataset encompasses a larger proportion of the ocean's variability than previously used datasets, it does not cover the whole range of variability of observed remote sensing reflectance (Rrs). Thus, using algorithms tuned to this more comprehensive dataset may still result in a temporal and/or geographical bias in global application. To address this generalization issue, we evaluated a variety of analytical algorithms based on radiative transfer theory and settled on a specific one. This algorithm computes Kd(λ) from inherent optical properties (IOPs) obtained from an Rrs inversion and information about the angular distribution of the radiance transmitted through the air/ocean interface. The resulting Kd(λ) estimates at 412 and 490 nm were not appreciably biased against the float measurements. Evaluation using other in-situ datasets and radiative transfer simulations was also satisfactory. Statistical performance was good in both clear and turbid waters. Further work should be conducted to examine whether the tuned algorithms and/or the new analytical algorithm demonstrate adequate hyperspectral performance.