The small-scale structure of grid turbulence is studied primarily using data obtained with a transverse vorticity (ω3) probe for values of the Taylor-microscale Reynolds number Rλ in the range 27–100. The measured spectra of the transverse vorticity component agree within ±10% with those calculated using the isotropic relation over nearly all wavenumbers. Scaling-range exponents of transverse velocity increments are appreciably smaller than exponents of longitudinal velocity increments. Only a small fraction of this difference can be attributed to the difference in intermittency between the locally averaged energy dissipation rate and enstrophy fluctuations. The anisotropy of turbulence structures in the scaling range, which reflects the small values of Rλ, is more likely to account for most of the difference. All four fourth-order rotational invariants Iα (α = 1 to 4) proposed by Siggia (1981) were evaluated. For any particular value of α, the magnitude of the ratio Iα / I1 is approximately constant, independently of Rλ. The implication is that the invariants are interdependent, at least in isotropic and quasi-Gaussian turbulence, so that only one power-law exponent may be sufficient to describe the Rλ dependence of all fourth-order velocity derivative moments in this type of flow. This contrasts with previous suggestions that at least two power-law exponents are needed, one for the rate of strain and the other for vorticity.