Before revision:  We use the geometric insight from our lower bound analysis to construct Steiner (1+ \epsilon )-spanners of lightness O( \epsilon ^{-1}\log n) for n points in Euclidean plane.
After revision:  We use the geometric insight from our lower bound analysis to construct Steiner (1+ \varepsilon )-spanners of lightness O( \epsilon ^{-1}\log n) for n points in Euclidean plane.