Kazhdan-Lusztig ideals encode neighborhoods of Schubert varieties. Alexander Woo (St. Olaf College) and I proved a Grobner basis theorem for them that geometrically interprets certain wiring configurations, and their appearance in formulae for Schubert and Grothendieck polynomials. It is an open problem to find a counting rule for multiplicities of Schubert sub-varieties of the flag variety. Recently, Li Li (U. Illinois) and I hypothesized the existence of a different Grobner basis, possessing good properties for this purpose. I'll report on our proof of this conjecture for the class of (co)vexillary Schubert varieties, and how it leads to multiplicity rules, both combinatorial and determinantal.