Knowledge of B 1+ distribution is crucial for many applications, such as quantitative MRI. A novel method has been developed to improve the accuracy of the conventionally applied double-angle method for B 1+ mapping. It solves the remaining issues raised by the use of selective pulses for slice selection to accelerate the acquisition process. A general approach for reconstructing B 1+ maps is presented first. It takes B 1+-induced slice profile distortions over off-resonance frequencies into account. It is then shown how the ratio between the prescribed flip angles can be adjusted to reach a compromise between the level of noise propagated onto B 1+ maps and the width of the range in which the field can be mapped. Lastly, several solutions are proposed for reducing the B 1+-dependent pollution of regions distal to the image slice which participates significantly in the inaccuracy of B 1+ mapping. These methods were experimentally tested by comparison with gold standard B 1+ maps obtained on a phantom using a non-selective and thus much slower technique. As they are independent and lead to significant improvements, these solutions can be combined to achieve high precision and fast B 1+ mapping using spin-echo DAM.