Let M be a closed pseudohermitian 3-manifold. We show a compactness criterion for contact forms in a fixed CR structure(i.e., conformal pseudohermitian structures), assuming a volume bound and L^p bounds on the Tanaka-Webster curvature and the pseudohermitian torsion. As an application, we can show that the CR automorphism group is compact if M is not CR spherical or the CR Yamabe constant is negative.