Let $K(\beta)$ be the class of normalised close-to-convex functions with order $\beta\ge0$, defined in the unit disc $D$ by $$ łeft|\arg e^{iłambda}\dfrac{zf'(z)}{g(z)}\right|łe\dfrac{\pi\beta}{2}, $$ for $|\lambda|<\pi/2$ and $g$ starlike in $D$. For $f\in K(\beta)$ with $f(z)=z+a_2z^2+a_3z^3+\cdots$ and $z\in D$, sharp bounds are given for $|a_3-\mu a_2^2|$ for real $\mu$.