We discuss the convergence of level truncation in bosonic open string field theory. As a test case we consider the calculation of the quartic tachyon coupling γ₄. We determine the exact contribution from states up to level L = 28 and discuss the L∞ extrapolation by means of the BST algorithm. We determine in a self-consistent way both the coupling and the exponent ω of the leading correction to γ₄ at finite L that we assume to be ∼ 1/L^ω. The results are γ₄ = −1.7422006(9) and |ω−1|≲10⁻⁴.