The JASON report about which I previously blogged, has an informative paragraph about the significance of the 20% U-235 threshold:

The choice of 20% enrichment to define LEU comes from tests and calculations carried out in the early 1950s, which indicated that a nuclear weapon could not be built using uranium enriched to less than 20%. Uranium at 20.1% enrichment is not significantly more weapons-usable than at 19.9%- there is no sharp physics threshold… there are no thresholds near the 20% enrichment level that would affect design or construction of a nuclear weapon. We needn’t worry about someone making a weapon with 19.99%-enriched uranium and the same is true for enrichments of 21% or 22%.