The author derives maximal pointwise Hölder estimates for Kohn’s Laplacian on strongly pseudoconvex CR manifolds of class \(C^3\) using the Tanaka-Webster pseudohermitian metric. Based on this she proves the following improved version of L. Boutet de Monvel’s embedding theorem [Séminaire Goulaouic-Lions-Schwartz, Exposé No. 9, 1974-1975 (1975; Zbl 0317.58003)]: If \(M\) is a compact, strongly pseudoconvex CR manifold with real dimension \(2n+1\), \(n\geq 2\), of class \(C^{3,\alpha}\), where \(0<\alpha<1\) then there exist global CR functions \(h_1,\dots, h_N\in C_*^{2,\alpha}(M)\) such that \(\Phi=(h_1,\dots, h_N): M\to \mathbb C^N\) is an embedding.