The influence of the finite thickness and structure, amorphous or crystalline, of Fe electrodes on the tunneling magnetoresistance (TMR) ratio is investigated by ab initio calculations in Fe/MgO/Fe tunnel junctions. An amorphous Fe layer in direct contact with the MgO barrier causes a low TMR ratio of only 44%. By inserting crystalline Fe monolayers between the barrier and the amorphous Fe the TMR ratio increases rapidly and reaches the same level as for semi-infinite Fe electrodes. Even one crystalline Fe monolayer is sufficient to achieve a giant TMR ratio exceeding 500%. Omitting the amorphous Fe has nearly no influence on the results if there are more than two monolayers of crystalline Fe next to the barrier. The results demonstrate that the reservoirs can even be nonmagnetic. The TMR emerges from the interplay of symmetry selection in the barrier and spin filtering at the electrode-barrier interface.