In this paper, we develop two improved retrieval algorithms of snow water equivalent (SWE) based on the volume scattering snow at X (9.6 GHz) and Ku (17.2 GHz) bands. Significantly, neither algorithm requires a prior on grain size nor scattering albedo. The two algorithms are validated with 4 sets of airborne data and 3 years of tower time series measurements. The two algorithms are based on improvements of the previous algorithm published in the previous two papers [1,2]. The physical model is the bi-continuous DMRT model, and a parametrization is carried out over a look-up table of DMRT results. The parameterized model gives the X and Ku band copolarization backscatter as a pair of equations in terms of two parameters SWE and scattering albedo at X band (ωX ). The solution space of two measurements and two parameters has been carefully studied. By directly inverting the pair of equations for, σ X (SW E, ωX ) and σ Ku (SW E, ωX ) we show that there are at most a pair of solutions which have SWE values that are far apart in most cases, facilitating identification of the correct solution. The first algorithm described in this paper, labeled algebraic algorithm, uses inversion alone and does not employ a cost function. The robustness of the no-prior approach was validated with the airborne observations, by using a prior SWE value that is intentionally far (75% different) from the true SWE. For the validation using tower-based data, time series observations from the NoSREx experiment in Sodankyla, Finland were used in which the SWE of the previous time step is used to correctly choose between the two solutions for the current time step. the second cost function-based algorithm finds the SWE and ωX pair which minimizes the difference between the observed volume scattering σ X,obs and σ Ku,obs and the model-predicted volume scattering σ X,mod and σ Ku,mod . The cost function uses prior information on SWE, also based on a time series starting with zero/low SWE. NoSREx data is used to show results from this approach. The new algorithm combined with time series eliminates the need for ancillary information of SWE and grain sizes, making the algorithm useful for level-2 products of a satellite mission.