  We establish a new version of the CR almost Schur Lemma which gives an
estimation of the pseudohermitian scalar curvature on a compact strictly
pseudoconvex pseudohermitian manifold to be a constant in terms of the norm of
the traceless Webster Ricci tensor and the pseudohermitian torsion under a
certain positivity condition. In the torsion-free case, i.e. for a compact
Sasakian manifold, our positivity condition coincides with the known one and we
obtain a better estimate
