We reexamine the general synchrotron model for gamma-ray bursts' (GRBs') prompt emission and determine the regime in the parameter phase space in which it is viable. We characterize a typical GRB pulse in terms of its peak energy, peak flux, and duration and use the latest Fermi observations to constrain the high-energy part of the spectrum. We solve for the intrinsic parameters at the emission region and find the possible parameter phase space for synchrotron emission. Our approach is general and it does not depend on a specific energy dissipation mechanism. Reasonable synchrotron solutions are found with energy ratios of 10-4 < εB /εe < 10, bulk Lorentz factor values of 300 < Γ < 3000, typical electrons' Lorentz factor values of 3 × 103 < γe < 105, and emission radii of the order 1015 cm < R < 1017 cm. Most remarkable among those are the rather large values of the emission radius and the electron's Lorentz factor. We find that soft (with peak energy less than 100 keV) but luminous (isotropic luminosity of 1.5 × 1053) pulses are inefficient. This may explain the lack of strong soft bursts. In cases when most of the energy is carried out by the kinetic energy of the flow, such as in the internal shocks, the synchrotron solution requires that only a small fraction of the electrons are accelerated to relativistic velocities by the shocks. We show that future observations of very high energy photons from GRBs by CTA could possibly determine all parameters of the synchrotron model or rule it out altogether.