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In this article, a robust methodology for in vivo T₁ mapping is presented. The approach combines a gold standard scanning procedure with a novel fitting procedure. Fitting complex data to a five‐parameter model ensures accuracy and precision of the T₁ estimation. A reduced‐dimension nonlinear least squares method is proposed. This method turns the complicated multi‐parameter minimization into a straightforward one‐dimensional search. As the range of possible T₁ values is known, a global grid search can be used, ensuring that a global optimal solution is found. When only magnitude data are available, the algorithm is adapted to concurrently restore polarity. The performance of the new algorithm is demonstrated in simulations and phantom experiments. The new algorithm is as accurate and precise as the conventionally used Levenberg‐Marquardt algorithm but much faster. This gain in speed makes the …