In his two pioneering articles [9, 10] Jerry Levine introduced
and completely determined the algebraic concordance groups
of odd dimensional knots. He did so by defining a host of
invariants of algebraic concordance which he showed were a
complete set of invariants. While being very powerful, these
invariants are in practice often hard to determine, especially
for knots with Alexander polynomials of high degree. We thus
propose the study of a weaker set of invariants of algebraic
concordance---the rational Witt classes of knots. Though these
are rather weaker invariants than those defined by Levine,
they have the advantage of lending themselves to quite manageable
computability. We illustrate this point by computing the rational
Witt classes of all pretzel knots. We give many examples and
provide applications to obstructing sliceness for pretzel
knots. Also, we obtain explicit formulae for the determinants
and signatures of all pretzel knots. This article is dedicated
to Jerry Levine and his lasting mathematical legacy; on the
occasion of the conference ``Fifty years since Milnor and
Fox'' held at Brandeis University on June 2--5, 2008.