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We study the one-dimensional Fisher–KPP equation, with an initial condition u 0 (x) that coincides with the step function except on a compact set. A well-known result of Bramson in [Maximal displacement of branching Brownian motion, Comm. Pure Appl. Math. 31 (1978) 531–581; Convergence of Solutions of the Kolmogorov Equation to Travelling Waves (American Mathematical Society, Providence, RI, 1983)] states that, as t → + ∞ , the solution converges to a traveling wave located at the position X (t) = 2 t − (3 / 2) log t + x 0 + o (1) , with the shift x 0 that depends on u 0 . Ebert and Van Saarloos have formally derived in [Front propagation into unstable states: Universal algebraic convergence towards uniformly translating pulled fronts, Phys. D 146 (2000) 1–99; Front propagation into unstable states, Phys. Rep. 386 (2003) 29–222] a correction to the Bramson shift, arguing that  X (t) = 2 t − (3 / 2) log t + x 0 − 3 π / t + O (1 / t). Here, we prove that this result does hold, with an error term of the size O (1 / t 1 − γ) , for any γ > 0. The interesting aspect of this asymptotics is that the coefficient in front of the 1 / t -term does not depend on u 0 . [ABSTRACT FROM AUTHOR]