Gradient coils reduce available bore space, incur costs, and create acoustic noise, but their encoding ability requires them to be present in MRI. The encoding strategy introduced here (FREE) removes the reliance on these coils by using a B1-gradient to create a spatially-dependent nutation frequency. Double spin-echoes created with adiabatic full-passage pulses generate magnetization phase proportional to the difference in their time-bandwidth products (R). Modulating the R-value of one of these π pulses traverses k-space similar to standard MRI. Adiabatic pulses make this approach highly tolerant to B0 and B1 inhomogeneity. A family of new sequences using FREE is presented.