The Look-Locker echo-planar imaging (LL-EPI) sequence has been numerically optimized in terms of the signal-to-noise ratio in the measured value of T1, for both single-shot (repetition time (TR) = infinity), and dynamically repeated T1 measurements. The sequence is optimized for the normal biologic range of T1 (0.2 s to 2.0 s) and for a range of sequence parameters found on most magnetic resonance (MR) scanners. Both linearly and geometrically spaced magnetization sample pulse intervals were considered. For single-shot measurements, the sequence with 24 linearly spaced sample pulses, an inversion time of 0.01 s, an inter-sample pulse delay of 0.10 s, and a sample radiofrequency (RF) pulse flip angle of 25 degrees was found to be optimum. When the number of sample pulses was limited due to hardware limitations, different pulse sequence parameters were indicated. The optimization procedures used are appropriate for any single-shot T1 mapping sequence variant and for any rapid T1 mapping application. The use of an optimized Look-Locker echo-planar imaging sequence is demonstrated by an example of dynamic contrast-enhanced scanning in the brain using fast T1 mapping.