A nonlinear finite-difference inverse model is used for estimating the North Atlantic general circulation between 20° and 50°N. The inverse model with grid spacing 2° latitude and 2.5° longitude is based on hydrography and is in geostrophic and hydrostatic balances. The constraints of the inverse model are surface and subsurface float mean velocities; Ekman pumping derived from wind data; conservations of mass, heat, and salt; and the planetary vorticity equation at the reference level. The mass, heat, and salt conservations are applied in a vertically integrated form. The model does not have explicit mixing or air–sea flux terms. Vertical velocities result from the nondivergence of the 3D velocity field. After inversion, float velocities, hydrographic data, and dynamical constraints are generally compatible within error bounds. A few float velocities are, however, rejected by the model mainly due to inadequate time or space sampling of the 2° latitude by 5° longitude boxes for which mean float velocities are computed. The resulting circulation shows a maximum Gulf Stream transport close to 130 × 106 m3 s−1 at 64°W. Residuals of the vertically integrated heat and salt conservation constraints may be interpreted as air–sea fluxes and are of the right order of magnitude as compared to in situ measurements. The float database used is already important particularly at the surface. However, its addition to the inversion does not change substantially the estimation by the model of integrated quantities, such as Gulf Stream transports, as compared to an inversion using hydrography and dynamical constraints alone. But floats significantly affect the estimation of the deep circulation increasing, for instance, the estimated velocity amplitude for the deep western boundary current flowing westward south of the Grand Banks.