A new method for B1-insensitive water suppression using adiabatic RF pulses is described. The transition zone of the inversion profile of adiabatic full passage (AFP) pulses is used for frequency-selective excitation followed by dephasing of the excited water with magnetic field gradients. Several improvements of AFP pulses, which also have implications for other applications, are described. The technique was evaluated by simulations based on the Bloch equations (including relaxation), in vitro experiments and an in vivo verification on neonatal and adult rat brain.