A method for injection of an imaging contrast into a patient, includes: a. in a first phase, injecting a fluid having a first concentration of contrast agent for a first period of time and b. in a second phase, injecting a fluid having a second concentration of contrast agent for a second period of time. The osmolarity of the second phase is higher than the osmolarity of the first phase. In several embodiments in which the contrast agent of the first phase is of the same composition as the contrast agent of the second phase, the second concentration can be higher than the first concentration. The first phase can, for example, precede the second phase. The method can further include: c. in a third phase, subsequent to the second phase, injecting a fluid having a third concentration of contrast agent for a third period of time. The osmolarity of the third phase is lower than the osmolarity of the second phase. In embodiments in which the composition of the contrast agent of the third phase is the same as the composition of the contrast agent of the second phase, the third concentration can be lower than the second concentration. The fluid injected in the first phase can, for example, be closer to the osmolarity of blood that the fluid injected in the second phase and can even be generally iso-osmolar to blood plasma (for example, within 20% or even 10% or less of the osmolarity of blood plasma of the patient). Likewise, the fluid injected in the third phase can be closer to the osmolarity of blood plasma that the fluid injected in the second phase and can even be generally iso-osmolar to blood.