(joint work with Dror Bar-Natan) In knot theory there are many invariants available but most are either very weak or very hard to compute. Using the theory of contractions of Lie groups we are able to reduce the computational complexity of quantum group invariants dramatically while retaining much of their strength. In the case of of sl(2) our reduction is conjectured to be related to the loop expansion of the colored Jones polynomial, the first term of which is the Alexander polynomial. Time permitting potential applications to genus and other classical invariants will be mentioned.