The invention relates to a method for the dehydration of, and in-line removal of asphaltenes from, heavy and extra-heavy crudes. The method is performed at the well head at pressures of between 414 and 689 KPa and temperatures of between 60 and 100° C. and includes two phases, namely a dehydration phase and a deasphalting phase. The first phase includes the addition of solvent, removal of free water, heating, addition of emulsion breakers and settling for removal of emulsified water. The asphaltenes are extracted in the second phase. Said phase comprises the use of low-force in-line static mixers and contactors having a specific design and a sedimentation device with specific internal arrangements for separation. The recovered solvent is recirculated into the method, the improved crude is separated and the asphaltenes are used as fuel for cogeneration which supplies the energy requirements for production and the improvement method.