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Let be an elliptic curve over a number field , or a nonconstant elliptic surface (elliptic curve over a function field ), and a point of nonzero canonical height on . Let be in the former case, and the discriminant degree of in the latter. Lang conjectured that there exists a constant such that . Hindry and Silverman proved this under the ABC conjecture for ; in particular they proved it unconditionally for an elliptic surface. The constant obtained by Hindry and Silverman, though explicit, is very small - less than - but is essentially the best that the analysis of Hindry and Silverman can yield. We review this analysis and give two improvements that together improve to about . We also explain how the same ideas lead to the conjecture that the correct value is (approximately ), and compare this with numerical data for explicit with low in the cases and .