The merger of close double white dwarfs (CDWDs) is one of the favourite evolutionary channels for producing Type Ia supernovae (SN Ia). Unfortunately, current theories of the evolution and formation of CDWDs are still poorly constrained and have several serious uncertainties, which affect the predicted SN Ia rates. Moreover, current observational constraints on this evolutionary pathway for SN Ia mainly rely on only 18 double-lined and/or eclipsing CDWDs with measured orbital and stellar parameters for both white dwarfs. In this paper we present the orbital periods and the individual masses of three new double-lined CDWDs, derived using a new method. This method employs mass ratios, the Halpha core ratios and spectral model-fitting to constrain the masses of the components of the pair. The three CDWDs are WD0028-474 (Porb=9.350 +- 0.007 hours, M1=0.60 +- 0.06 Msun, M2=0.45 +- 0.04 Msun), HE0410-1137 (Porb = 12.208 +- 0.008 hours, M1= 0.51 +- 0.04 Msun, M2= 0.39 +- 0.03 Msun) and SDSSJ031813.25-010711.7 (Porb = 45.908 +- 0.006 hours, among the longest period systems, M1= 0.40 +- 0.05 Msun, M2= 0.49 +- 0.05 Msun). While the three systems studied here will merge in timescales longer than the Hubble time and are expected to become single massive (>~0.9 Msun) white dwarfs rather than exploding as SN Ia, increasing the small sample of CDWDs with determined stellar parameters is crucial for a better overall understanding of their evolution.