This work studies the effect of diffusion-weighting on the precision of measurements of the apparent diffusion coefficient (ADC, or D) by diffusion-weighted magnetic resonance imaging. The precision in the value of the ADC was described in terms of a diffusion-to-noise ratio (DNR) which was calculated as the signal-to-noise ratio in the resultant ADC. A theoretical analysis decomposed the DNR into the signal-to-noise ratio in the diffusion-weighted image and the sensitivity of diffusion-weighting, "KD". The latter reflects the effect of the sampling strategy in the diffusion-weighting domain on the DNR. The theoretical analysis demonstrated that optimal two-point diffusion-weighting could be achieved in the vicinity of zeta = D(b2-b1) = 1.1, where zeta is a non-dimensional parameter of diffusion-weighting, and b1 and b2 are the diffusion-weighting factors for the two-point diffusion-weighting. This approach also derived an optimised signal averaging scheme. The limitations and restrictions of the two-point scheme for in vivo ADC measurement were also considered; these included a detailed discussion on partial volume effects. The theory was verified by experiments on phantoms and on the brain of a healthy volunteer using a diffusion-weighted echo-planar imaging protocol. This led to an optimal two-point diffusion-weighting for ADC measurement in human brain using b1 = 300, and b2 = 1550 +/- 100 s/mm2. Such a two-point scheme successfully measured values of the ADC in gray matter, white matter and cerebrospinal fluid in human brain. It thus offers an alternative to the commonly used multiple-point schemes and has the advantage of requiring significantly shorter imaging times.