(17)O MAS NMR spectra recorded at 14.1T and room temperature (RT) for (17)O-enriched samples of the two perrhenates, KReO4 and NH4ReO4, exhibit very similar overall appearances of the manifold of spinning sidebands (ssbs) for the satellite transitions (STs) and the central transition (CT). These overall appearances of the spectra are easily simulated in terms of the usual quadrupole coupling and chemical shift interaction parameters. However, a detailed inspection of the line shapes for the individual ssbs of the STs and, in particular, for the CT in the spectrum of KReO4 reveals line-shape features, which to our knowledge have not before been observed experimentally in 1D MAS NMR spectra for any quadrupolar nucleus, nor emerged from simulations for any combination of second-order quadrupolar interaction and chemical shift anisotropy. In contrast, such line-shape features are not observed for the corresponding ssbs (STs and CT) in the 14.1T RT (17)O MAS NMR spectrum of NH4ReO4. Considering the additional interaction of a combination of residual heteronuclear (17)O-(185/)(187)Re dipolar and scalar J coupling between this spin pair of two quadrupolar nuclei, spectral simulations for KReO4 show that these interactions are able to account for the observed line shapes, although the expected (1)J((17)O-(185/)(187)Re) six-line spin-spin splittings are not resolved. Low-temperature, high-field (21.1T) (17)O VT MAS NMR spectra of both KReO4 and NH4ReO4 show that full resolution into six-line multiplets for the centerbands are achieved at -90°C and -138°C, respectively. This allows determination of (1)J((17)O-(187)Re)=-268Hz and -278Hz for KReO4 and NH4ReO4, respectively, i.e., an isotropic (1)J coupling and its sign between two quadrupolar nuclei, observed for the first time directly from solid-state one-pulse 1D MAS NMR spectra, without resort to additional 1D or 2D experiments. Determination of T1((187)Re) spin-lattice relaxation times, observed indirectly through a 2D (17)O EXSY experiment for NH4ReO4 at several low temperatures, show that the dynamics observed for the ReO4(-) anion in the (17)O VT MAS NMR spectra at low temperatures are caused by self-decoupling of (1)J((17)O-(187)Re). The (1)J((17)O-(187)Re) values determined here for ReO4(-) from solid-state (17)O MAS NMR, along with literature (1)J((17)O-M) values for oxoanions (M being a quadrupolar nucleus) obtained from liquid-state NMR, have allowed correlations to be established between the reduced coupling constant (1)K((17)O-M)=2π(1)J((17)O-M)/(γ17OγMℏ) and the atomic number of M.