This paper presents a combination of speculative approaches, some related to earlier work and some apparently novel, which show great promise in providing a new class of MRI machines that would be considerably less expensive. This class would have advantages and disadvantages as compared to existing MRI, over and above that of low cost. The disadvantages include the apparent inability to perform classic spectroscopy, and limited flexibility in the area of selective excitation. The advantages include a fundamental immunity to inhomogeneity and susceptibility problems, the ability to create a wide class of machines that are designed for specific anatomy-related applications, the ability to design open machines for physician access, and improved capability for high speed imaging. Generic to all of the methods presented are a pulsed polarizing field and an oscillatory read-out bias field. The pulsed field initially polarizes the magnetic moments. Since it is not on during the readout operation it has negligible homogeneity requirements since changes in the field amplitude will merely shade the image intensity. During readout a relatively low bias field is used. To enable the use of a relatively inhomogeneous bias field, an oscillatory field is used that has a zero average value. This prevents any long-term buildup of phase errors due to a frequency error associated with inhomogeneity. Thus the average bias frequency will be determined solely by the frequency rather than the amplitude of the bias field. Three methods are described, all including the above features. The first two involve imaging in the laboratory frame, while the third involves imaging in the rotating frame. The second approach requires no RF excitation and the third approach uses RF bias and gradient signals. Some approaches to slice selection are described.