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We consider the heterotic string on an elliptic Calabi-Yau three-fold withfive-branes wrapping curves in the base ('horizontal' curves) of the Calabi-Yauas well as some elliptic fibers ('vertical' curves). We show that in thisgeneralized set-up, where the association of the heterotic side with the$F$-theory side is changed relative to the purely vertical situation, thenumber of five-branes wrapping the elliptic fibers still matches thecorresponding number of $F$-theory three-branes.Comment: 21 pages harvmac, reference adde

Horizontal and vertical five-branes in heterotic/F-theory duality