  We prove a Lieb--Thirring inequality for Schr\"odinger operators
$-\frac{\mathrm{d}^2}{\mathrm{d}x^2}+V$ on the semi-axis with Robin boundary
condition at the origin. The result improves on a bound obtained by P.~Exner,
A.~Laptev and M.~Usman [Commun.~Math.~Phys. 362(2), 531--541 (2014)] albeit
under the additional assumption $V\in L^1(\mathbb{R}_+)$. The main difference
in our proof is that we use the double commutation method in place of the
single commutation method. We also establish an improved inequality in the case
of a Dirichlet boundary condition.
