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We ask whether Cohen and Glashow's very special relativity model for Lorentz violation might be modified, perhaps by quantum corrections, possibly producing a curved space-time with a cosmological constant. We show that its symmetry group ISIM (2) does admit a 2-parameter family of continuous deformations, but none of these give rise to noncommutative translations analogous to those of the de Sitter deformation of the Poincar\'e group: space-time remains flat. Only a 1-parameter family DISIM₁ (2) of deformations of SIM (2) is physically acceptable. Since this could arise through quantum corrections, its implications for tests of Lorentz violations via the Cohen-Glashow proposal should be taken into account. The Lorentz-violating point-particle action invariant under DISIM₁ (2) is of Finsler type, for which the line element is homogeneous of degree 1 in displacements, but anisotropic. We derive DISIM₁ (2) -invariant wave equations for particles of spins 0, 12, and 1. The experimental bound, |b|<10^-26, raises the question ``Why is the dimensionless constant b so small in very special relativity? ''
Gibbons et al. (2007) studied this question.