Certain physical problems lead to a need for quantization in a context where a Poisson bracket does not provide the direction. Nambu mechanics on a three-dimensional "phase space" is one example. Another is the problem of quantization on coadjoint orbits, especially on singular orbits. Abelian *-products are often governed by Harrison cohomology, but are erroneously said to be trivial. In fact, varieties with singularities, including simple examples of physical relevance, do have a nontrivial Harrison cohomology. Besides, Harrison cohomology is not always decisive. Minkowski space is a smooth manifold, with vanishing Harrison cohomology; the coordinate algebra admits, nevertheless, nontrivial Abelian deformations.