The ability of the Relaxed Eddy Accumulation (REA) method to estimate the kinematic fluxes of temperature, water vapor and carbon dioxide was assessed for the dry season (3 months) at the ATTO (Amazon Tall Tower Observatory) site from turbulence measurements. The measurements were performed at 50 m above ground within the roughness sublayer. Non-conformity with inertial sublayer conditions was confirmed one more time by analyzing dimensionless scalar standard deviations. Recently found results that the REA method outperforms Monin-Obukhov-based approaches are confirmed. Over the scale of the whole dry season, REA and EC (eddy covariance) estimates are essentially equal. However, we also verify that such results fail to reveal significant variability and scatter of the REA estimates when the fluxes are of small magnitude. On the basis of previous studies, we conjecture that this is caused by a likely imbalance between scalar gradient production and molecular dissipation. Confirmation of our results to trace gases, therefore, requires further study.