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Medium and high energy absorptive parts contribute to dispersive expressionsfor D- wave scattering lengths, $a^0_2$ and $a^2_2$. For the model employed byBasdevant, Frogatt and Peterson we find the D- wave driving term contributionsto the D- wave scattering lengths are $1.8\cdot 10^{-4}$ to $a^0_2$ and$0.4\cdot 10^{-4}$ to $a^2_2$, roughly $10\%$ and $30\%$ of their respective  central experimental values. Inequivalent sets of sum rules are used as acompelling test of the consistency of the model for which crossing symmetry isnot guaranteed. Results for the F- wave scattering length $a^1_3$ arepresented, completing the recent Roy equation analysis of \pipi scattering inthe range for $a^0_0$ favored by standard chiral perturbation theory.Comment: 31 pages plain latex to be run twice with 3 embedded figures using  eps

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Scattering lengths and medium and high energy<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>π</mml:mi><mml:mi>π</mml:mi></mml:math>scattering

Scattering lengths and medium and high energyππscattering