  We briefly report our recent construction of new fuzzy spheres of dimensions
d=1,2 covariant under the full orthogonal group O(D), D=d+1. They are built by
imposing a suitable energy cutoff on a quantum particle in D dimensions subject
to a confining potential well V(r) with a very sharp minimum on the sphere of
radius r=1; furthermore, the cutoff and the depth of the well depend on (and
diverge with) a natural number L. The commutator of the coordinates depends
only on the angular momentum, as in Snyder noncommutative spaces. When L
diverges, the Hilbert space dimension diverges, too; S^d_L converges to S^d,
and we recover ordinary quantum mechanics on S^d. These models might be useful
in quantum field theory, quantum gravity or condensed matter physics.
