Low-lying UV spectroscopy of trans-1,3-butadiene has been extensively studied by experimentalists and theorists. Though a host of techniques has been applied to understand its lowest electronic states, there are still important open questions. Among these are the positions of the two lowest valence excited states and the factors responsible for the spectral shape of the lowest allowed transitions. We present results from EOM-CC calculations in extended basis sets that are used to parametrize a three-electronic-state Koppel, Domcke, and Cederbaum (KDC) model. We test the sensitivity of the KDC model to a variety of parameters and address several outstanding questions regarding the spectrum. We find that the overall shape of the spectrum is determined primarily by the Franck-Condon envelope of the 1(1)B(u) state and that the princple impact of the doubly excited 2(1)A(g) state is to broaden the 1(1)B(u) peaks. There is only modest sensitivity to the relative position of these two states. We find that the lowest Rydberg state, the 1(1)B(g) state, has an unexpected impact on the third peak in the spectrum, and its effect is considerably more energy-dependent than that of the 2(1)A(g) state.