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We analyze the X-ray spectra of the atoll 4U~1705-44 when the sourceundergoes the island-banana state transition. We use the Rossi X-ray TimingExplorer (RXTE) and BeppoSAX observations for this analysis. We demonstratethat the broad-band energy spectral distributions for all evolutinary statescan be fitted by a model, consisting two Comptonized components. One arisesfrom the seed photons coming from a neutron star (NS) atmosphere at atemperature kT_{s1}<1.5 keV (herein Comptb) and a second resulting from theseed photons of T_{s2}~1.1-1.3 keV coming from the disk (herein Comptb2). Wefound that we needed to add a low-temperature blackbody and an iron-line({Gaussian}) component to the model in order to obtain high-quality fits. Thedata analysis using this model indicates that the power-law photon indexGamma_{1} of our model is always about 2, independently of the spectral state.Another parameter, Gamma_{2} demonstrates a two-phase behavior depending on thespectral state. Gamma_{2} is quasi-constant at Gamma_{2}~ 2 when the electrontemperature kT^{(2)}_e<80 keV and Gamma_{2} is less than 2, in the range of1.3<Gamma_{2}<2, when kT^{(2)}_e>80 keV. This phase is similar to that waspreviously found in the Z-source Sco X-1. We interpret the decreasing indexphase using a model in which a super-Eddington radiation pressure from theneutron star causes an expansion of the Compton cloud similar to that foundpreviously in Sco~X-1 during the Flaring branch.