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Thomassen conjectured that triangle-free planar graphs have exponentiallymany 3-colorings. Recently, he disproved his conjecture by providing examplesof such graphs with $n$ vertices and at most $2^{15n/\log_2 n}$ 3-colorings. Weimprove his construction, giving examples of such graphs with at most$64^{n^{log_{9/2} 3}}<64^{n^{0.731}}$ 3-colorings. We conjecture this exponentis optimal.

Triangle-free planar graphs with at most $64^{n^{0.731}}$ 3-colorings