The height of a rational number is the maximum of its denominator and numerator. It has been observed numerically that the logarithmic heights of rational iterates $(y_n)$ of discrete Painlev\'e equations are bounded by a power of $n$. This property, called "Diophantine integrability" appears to be a good detector of integrable discrete equations. Using well known properties of elliptic curves we show that the QRT map is Diophantine integrable. Some non-autonomous examples will then be discussed.