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Magnetic resonance imaging (MRI) is performed with a very large instrument that allows the patient to be inserted into a region of uniform magnetic field. The field is generated either by an electromagnet (resistive or superconductive) or by a permanent magnet. Electromagnets are designed as air cored solenoids of cylindrical symmetry, with an inner bore of 80–100 cm in diameter. In clinical analysis of peripheral regions of the body (legs, arms, foot, knee, etc.) it would be better to adopt much less expensive magnets leaving the most expensive instruments to applications that require the insertion of the patient in the magnet (head, thorax, abdomen, etc.). These “dedicated” apparati could be smaller and based on resistive magnets that are manufactured and operated at very low cost, particularly if they utilize an iron yoke to reduce power requirements. In order to obtain good field uniformity without the use of a set of shimming coils, we propose both particular construction of a dedicated magnet, using four independently controlled pairs of coils, and an optimization-based strategy for computing, a posteriori, the optimal current values. The optimization phase could be viewed as a low-cost shimming procedure for obtaining the desired magnetic field configuration. Some experimental measurements, confirming the effectiveness of the proposed approach (construction and optimization), have also been reported. In particular, it has been shown that the adoption of the proposed optimization based strategy has allowed the achievement of good uniformity of the magnetic field in about one fourth of the magnet length and about one half of its bore. On the basis of the good experimental results, the dedicated magnet can be used for MRI of peripheral regions of the body and for animal experimentation at very low cost. © 2000 American Institute of Physics.