Time-resolved spectral analysis, though a very promising method to understand the emission mechanism of gamma-ray bursts (GRBs), is difficult to implement in practice because of poor statistics. We present a new method for pulse-wise time-resolved spectral study of the individual pulses of GRBs, using the fact that many spectral parameters are either constants or smooth functions of time. We use this method for the two pulses of GRB 081221, the brightest GRB with separable pulses. We choose, from the literature, a set of possible models which includes the Band model, blackbody with a power-law (BBPL), a collection of black bodies with a smoothly varying temperature profile, along with a power-law (mBBPL), and two blackbodies with a power-law (2BBPL). First, we perform time-resolved study to confirm the spectral parameter variations, and then construct the new model to perform a joint spectral fit. We find that any photospheric emission in terms of black bodies is required mainly in the rising parts of the pulses and the falling part can be adequately explained in terms of the Band model, with the low energy photon index within the regime of synchrotron model. Interestingly, we find that 2BBPL is comparable or sometimes even better, though marginally, than the Band model, in all episodes. Consistent results are also obtained for the brightest GRB of Fermi era --- GRB 090618. We point out that the method is generic enough to test any spectral model with well defined parameter variations.
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